REFERENCES ON MULTIPLE ZETA VALUES AND EULER SUMS

Compiled by Michael Hoffman

The list is in (approximate) chronological order within each category. While the categorization of some works is a bit arbitrary, I have generally tried to place each one in the most inclusive category that seemed appropriate.

This list is revised regularly. Report errors and omissions to meh@usna.edu.

Author index

A. DOUBLE HARMONIC SERIES

P. H. Fuss (ed.), Correspondance Mathématique et Physique de quelques célèbres Géomètres (Tome 1), St. Petersburg, 1843.
L. Euler, `Meditationes circa singulare serierum genus,' Novi Comm. Acad. Sci. Petropol. 20 (1776), 140-186. Reprinted in Opera Omnia, ser. I, vol. 15, B. G. Teubner, Berlin, 1927, pp. 217-267.
N. Nielsen, Die Gammafunktion, Chelsea, New York, 1965. Reprint of Handbuch der Theorie der Gammafunktion (1906) and Theorie der Integrallogarithmus und verwandter Transzendenten (1906).
F. V. Atkinson, `The mean value of the Riemann zeta function,' Acta Math. 81 (1949), 353-376.
L. Tornheim, `Harmonic double series,' Amer. J. Math. 72 (1950), 303-314.
G. T. Williams, `A new method of evaluating ζ(2n),' Amer. Math. Monthly 60 (1953), 19-25.
P. F. Jordan, `Infinite sums of psi functions,' Bull. Amer. Math. Soc. 79 (1973), 681-683.
T. M. Apostol and T. H. Vu, `Dirichlet series related to the Riemann zeta function,' J. Number Theory 19 (1984), 85-102.
M. V. Subbarao and R. Sitaramachandrarao, `On some infinite series of L. J. Mordell and their analogues', Pacific J. Math. 119 (1985), 245-255.
D. Zagier, `Periods of modular forms, traces of Hecke operators, and multiple zeta values,' in Research into automorphic forms and L functions (Kyoto, 1992), Sūrikaisekikenyūsho Kōkyūroku 843 (1993), pp. 162-170.
R. E. Crandall and J. P. Buhler, `On the evaluation of Euler sums,' Experiment. Math. 3 (1994), 275-285.
D. Borwein and J. M. Borwein, `On an intriguing integral and some series related to ζ(4),' Proc. Amer. Math. Soc. 123 (1995), 1191-1198.
L-C. Shen, `Remarks on some integrals and series involving the Stirling numbers and ζ(n)', Trans. Amer. Math. Soc. 347 (1995), 1391-1399.
J. G. Huard, K. S. Williams, and N-Y. Zhang, `On Tornheim's double series,' Acta Arithmetica 75 (1996), 105-117.
M-A. Coppo, `Sur les sommes d'Euler divergentes,' Expositiones Mathematicae 18 (2000), 297-308.
Wenchang Chu, `Symmetric functions and the Riemann zeta series,' Indian J. Pure Appl. Math. 31 (2000), 1677-1689.
A. Basu and T. M. Apostol, `A new method of investigating Euler sums,' Ramanujan J. 4 (2000), 397-419.
K. N. Boyadzhiev, `Evaluation of Euler-Zagier sums,' Internat. J. Math. Math. Sci. 27 (2001), 407-412.
K. N. Boyadzhiev, `Consecutive evaluation of Euler sums,' Internat. J. Math. Math. Sci. 29 (2002), 555-561.
H. Tsumura, `On some combinatorial relations for Tornheim's double series,' Acta Arithmetica 105 (2002), 239-252.
T. M. Rassias and H. M. Srivastava, `Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers,' Appl. Math. and Comp. 131 (2002), 593-605.
M. W. Coffey, `On some log-cosine integrals related to ζ(3), ζ(4), and ζ(6),' J. Comp. Appl. Math. 153 (2003), 205-215.
H. Tsumura, `On alternating analogues of Tornheim's double series,' Proc. Amer. Math. Soc. 131 (2003), 3633-3641.
H. Tsumura, `Evaluation formulas for Tornheim's type of alternating double series,' Math. Comp. 73 (2004), 251-258.
M. Jung, Y. J. Cho and J. Choi, `Euler sums evaluatable from integrals,' Commun. Korean Math. Soc. 19 (2004), 545-555.
H. Tsumura, `On evaluation formulas for double L-values,' Bull. Aust. Math. Soc. 70 (2004), 213-221.
D. Terhune, `Evaluation of double L-values,' J. Number Theory 105 (2004), 275-301.
R. Masri, `The Herglotz-Zagier function, double zeta values, and values of L-series,' J. Number Theory 106 (2004), 219-237.
K. Matsumoto, `Functional equations for double zeta-functions,' Math. Proc. Cambrige Philos. Soc. 136 (2004), 1-7.
M. W. Coffey, `On one-dimensional digamma and polygamma series related to the evaluation of Feynman diagrams,' J. Comp. Appl. Math. 183 (2005), 84-100.
D. M. Bradley, `A q-analog of Euler's decomposition formula for the double zeta function,' Internat. J. Math. Math. Sci. 2005 (2005), 3453-3458.
H. Tsumura, `Certain functional relations for the double harmonic series related to the double Euler numbers,' J. Aust. Math. Soc. 79 (2005), 319-333.
S. Kanemitsu, Y. Tanigawa, and M. Yoshimoto, `Convolution of multiple zeta values,' J. Math. Soc. Japan 57 (2005), 1167-1177.
O. Espinosa and V. H. Moll, `The evaluation of Tornheim double sums, Part I,' J. Number Theory 116 (2006), 200-229; preprint CA/0505647.
K-W. Chen and M. Eie, `Explicit evaluations of extended Euler sums,' J. Number Theory 117 (2006), 31-52.
D. Terhune, `Evaluations of a class of double L-values,' Proc. Amer. Math. Soc. 134 (2006), 1881-1889.
H. Tsumura, `On some functional relations between Mordell-Tornheim double L-functions and Dirichlet L-functions,' J. Number Theory 120 (2006), 161-178.
H. Gangl, M. Kaneko, D. Zagier, `Double zeta values and modular forms,' in Automorphic Forms and Zeta Functions, S. Böcherer et. al. (eds.), World Scientific, Singapore, 2006, pp. 71-106; preprint MPIM2005-96.
T. Nakamura, `A functional relation for the Tornheim zeta function,' Acta Arithmetica 125 (2006), 257-263.
I. Kiuchi and Y. Tanigawa, `Bounds for double zeta-functions,' Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 5 (2006), 445-464.
H. Tsumura, `On certain polylogarithmic double series,' Arch. Math. (Basel) 88 (2007), 42-51
H. Tsumura, `On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function,' Math. Proc. Cambridge Philos. Soc. 142 (2007), 395-405.
J. M. Borwein, `Hilbert's inequality and Witten's zeta-function,' Amer. Math. Monthly 115 (2008), 125-137.
M. W. Coffey, `On a three-dimensional symmetric Ising tetrahedron and contributions to the theory of the dilogarithm and Clausen functions,' J. Math. Phys. 49 (2008), art. 043510 (32 pp).
X. Zhou, T. Cai, and D. M. Bradley, `Signed q-analogs of Tornheim's double series,' Proc. Amer. Math. Soc. 136 (2008), 2689-2698.
M. Kuba, `On evaluations of infinite double sums and Tornheim's double series,' Sém. Lothar. Combin. 58 (2008), art. B58d (13 pp).
J. M. Borwein, I. J. Zucker, and J. Boersma, `The evaluation of character Euler double sums,' Ramanujan J. 15 (2008), 377-405.
A. Basu, `A new method in the study of Euler sums,' Ramanujan J. 16 (2008), 7-24.
Y. Komori,`An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers,' Ramanujan J. 17 (2008), 163-183.
K. N. Boyadzhiev, H. Gopalkrishna Gadiyar, and R. Padma, `The values of an Euler sum at the negative integers and a relation to a certain convolution of Bernoulli numbers,' Bull. Korean Math. Soc. 45 (2008), 277-283.
K. Matsumoto and H. Tsumura, `Functional relations among certain double polylogarithms and their character analogues,' Šialiai Math. Semin. 3(11) (2008), 189-205.
T. Nakamura, `Double Lerch value relations and functional relations for Witten zeta functions,' Tokyo J. Math. 31 (2008), 551-574.
T. Nakamura, `Double Lerch series and their functional relations,' Aequationes Math. 75 (2008), 251-259.
H. Tsumura, `On alternating analogues of Tornheim's double series II', Ramanujan J. 18 (2009), 81-90.
T. Nakamura, `Restricted and weighted sum formulas for double zeta values of even weight,' Šialiai Math. Semin. 4(12) (2009), 151-155.
M. Eie and W-C. Liaw, `Double Euler sums on Hurwitz zeta functions,' Rocky Mountain J. Math. 39 (2009), 1869-1883.
K. N. Boyadzhiev, H. Gopalkrishna Gadiyar, and R. Padma, `Alternating Euler sums at the negative integers,' Hardy-Ramanujan J. 32 (2009), 24-37; preprint 0811.4437[NT].
J. Furuya and Y. Tanigawa, `Analytic properties of Dirichlet series obtained from the error term in the Dirichlet divisor problem,' Pacific J. Math. 245 (2010), 239-254.
Y. Komori, K. Matsumoto, and H. Tsumura, `Functional equations and functional relations for the Euler double zeta-function and its generalization of Eisenstein type,' Publ. Math. Debrecen 77 (2010), 15-31.
O. Espinosa and V. H. Moll, `The evaluation of Tornheim double sums, Part II,' Ramanujan J. 22 (2010), 55-99; preprint 0811.0557[NT].
J. Zhao, `A note on colored Tornheim's double series,' Integers 10 (2010), #A59, 879-882.
I. Kiuchi, Y. Tanigawa, and W. Zhai, `Analytic properties of double zeta-functions,' Indag. Math. (N. S.) 21 (2011), 16-29.
A. Basu, `On the evaluation of Tornheim sums and allied double sums,' Ramanujan J. 26 (2011), 193-207.
T. Okamoto, `Some relations among Apostol-Vu double zeta functions for coordinatewise limits at non-positive integers,' Tokyo J. Math. 34 (2011), 353-366.
Y. Komori, K. Matsumoto, and H. Tsumura, `Functional equations for double L-functions and values at non-positive integers, Int. J. Number Theory 7 (2011), 1441-1461.
P. Cartier, `On the double zeta values,' in Galois-Teichmüller Theory and Arithmetic Geometry, H. Nakamura et. al. (eds.), Adv. Studies in Pure Math. 68, Math. Soc. Japan, Tokyo, 2012, pp. 91-119; IHES preprint M-11-21.
T. Nakamura, `A simple proof of the functional equation for the Lerch type Tornheim double zeta function,' Tokyo J. Math. 35 (2012), 333-337.
T. Nakamura and K. Tasaka, `Remarks on double zeta values of level 2,' J. Number Theory 133 (2013), 48-54.
T. Machide, `Generators for vector spaces consisting of double zeta values with even weight,' J. Number Theory 133 (2013), 2240-2246; preprint 0802.1565[NT].
T. Machide, `Some restricted sum formulas for double zeta values,' Proc. Japan Acad. Ser. A Math. Sci. 89 (2013), 51-54.
J. Wan, `Some notes on weighted sum formulae for double zeta values,' in Number Theory and Related Fields: In Memory of Alf van der Poorten, J. M. Borwein et. al (eds.), Springer Proc. in Math. and Stat. 43, Springer, New York, 2013, pp. 361-379; preprint 1206.2424[NT].
S. Baumard and L. Schneps, `Period polynomial relations between double zeta values,' Ramanujan J. 32 (2013), 83-100; preprint 1109.3786[NT].
M. Kaneko and K. Tasaka, `Double zeta values, double Eisenstein series, and modular forms of level 2,' Math. Ann. 357 (2013), 1091-1118; preprint 1112.5697[NT].
D. M. Bradley and X. Zhou, `A q-analog of Euler's reduction formula for the double zeta function,' in Computation and Analytical Mathematics, D. H. Bailey et. al. (eds.), Springer Proc. in Math. and Stat. 50, Springer, New York, 2013, pp. 113-126.
Q. Tian, L. Ding, and Y. Mei, `Evaluation of a class of double L-values of Tornheim's type,' Adv. Math. (China) 42 (2013), 655-664.
K. Dilcher, Kh. Hessami Pilehrood, and T. Hessami Pilehrood, On q-analogues of double Euler sums,' J. Math. Anal. Appl. 410 (2014), 979-988.
K. Onodera, `A functional relation for Tornheim's double zeta functions,' Acta Arithmetica 162 (2014), 337-354; preprint 1211.1480[NT].
K. Matsumoto and M. Shōji, `Numerical computations on the zeroes of the Euler double zeta-function I,' Mosc. J. Comb. Number Theory 4 (2014), 21-39; preprint 1403.3765[NT].
T. Okamoto and T. Onozuka, `Mean value theorems for the Mordell-Tornheim double zeta function,' Ramanujan J. 37 (2015), 131-163.
S. Ikeda, K. Matsuoka, and Y. Nagata, `On certain mean values of the double zeta-function,' Nagoya Math. J. 217 (2015), 161-190; preprint 1303.6505[NT].
K. Matsumoto and H. Tsumura, `Mean value theorems for the double zeta-function,' J. Math. Soc. Japan 67 (2015), 383-406; preprint 1203.2242[NT].
S. Ikeda and K. Masuoka, `Double analogue of Hamburger's theorem,' Publ. Math. Debrecen 86 (2015), 89-98.
Z-h. Li,`On functional relations for the alternating analogues of Tornheim's double zeta function,' Chin. Ann. Math. Ser. B 36 (2015), 907-918; preprint 1011.2897[NT].
H. Yuan and J. Zhao, `Double shuffle relations of double zeta values and the double Eisenstein series at level N,' J. London Math. Soc. (2) 92 (2015), 520-546; preprint 1401.6699[NT].
T. Nakamura, `Real zeroes of Hurwitz-Lerch zeta and Hurwitz-Lerch type of Euler-Zagier double zeta functions,' Math. Proc. Cambridge Philos. Soc. 160 (2016), 39-50; preprint 1405.1504[NT].
Y. Choie and K. Matsumoto, `Functional equations for double series of Euler type with coefficients,' Adv. Math. 292 (2016), 529-557; preprint 1306.0987[NT].
D. Ma, `Inverse of some matrix related to double zeta values of odd weight,' J. Number Theory 166 (2016), 166-180; preprint 1510.06094[NT].
D. Ma, `Period polynomial relations between formal double zeta values of odd weight,' Math. Ann. 365 (2016), 345-362. preprint 1409.7717[NT].
Z. Shen and T. Cai, `Some weighted sum identities for double zeta values,' Acta Math. Sinica (Engl. Ser.) 32 (2016), 797-806.
S. Ikeda, I. Kiuchi, and M. Kaneaki, `Power moments for the double zeta-function,' Kumamoto J. Math. 29 (2016), 1-33.
I. Kiuchi and M. Minamide, `Mean square formula for the double zeta-function,' Funct. Approx. Comment. Math. 55 (2016), 31-43.
I. Kiuchi, `The fourth power moment of the double zeta-function,' Publ. Inst. Math. (Beograd) (N.S.) 100 (114) (2016), 229-241.
T. Nakamura, `Hurwitz-Lerch zeta and Hurwitz-Lerch type of Euler-Zagier double zeta distributions,' Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), art. 1650029 (12 pp.); preprint 1405.1799[NT].
X. Si, C. Xu, and M. Zhang, `Quadratic and cubic harmonic number sums,' J. Math. Anal. Appl. 447 (2017), 419-434.
D. Ma, `Period polynomial relations of binomial coefficients and binomial realization of formal double zeta space,' Int. J. Number Theory 13 (2017), 761-774.
C. Xu, M. Zhang, and W. Zhu, `Some evaluation of q-analogues of Euler sums,' Monatsh. Math. 182 (2017), 957-975.
D. Romik, `On the number of n-dimensional representations of SU(3), the Bernoulli numbers, and the Witten zeta function,' Acta Arithmetica 180 (2017), 111-159; preprint 1503.03776[NT].
S. Kadota, T. Okamoto, and K. Tasaka, `Evaluation of Tornheim's type of double series,' Illinois J. Math. 2 (2017), 171-186; preprint 1703.07471[NT].
Y. Choie and K. Matsumoto, `Functional equations for double series of Euler-Hurwitz-Barnes type with coefficients,' in Various Aspects of Multiple Zeta Values (Kyoto, 2013), K. Ihara (ed.), RIMS Kōkyūroku Bessatsu B68 (2017), pp. 91-109; preprint 1403.1940[NT].
M. Coffey, `Bernoulli identities, zeta relations, determinant expressions, Mellin transforms, and representation of the Hurwitz numbers,' J. Number Theory 184 (2018), 27-67; preprint 1601.01673[NT].
R. Harada, `On Euler's formulae for double zeta values,' Kyushu J. Math. 72 (2018), 15-24.
J. M. Borwein and K. Dilcher, `Derivatives and fast evaluation of the Tornheim zeta function, Ramanujan J. 45 (2018), 413-432.
D. Bannerjee, T. M. Minamide, and Y. Tanigawa, `Bounds of double zeta-functions and their applications,' Pacific J. Math. 304 (2020), 15-41.
X. Si and C. Xu, `Evaluations of some quadratic Euler sums,' Bull. Korean Math. Soc. 57 (2020), 489-508; preprint 1701.00389[NT].
K. Matsumoto and M. Shōji, `Numerical computations on the zeroes of the Euler double zeta-function II,' Eur. J. Math. 6 (2020), 488-507; preprint 1606.03806[NT].
Weijia Wang and H. Zhang, `On Mordell-Tornheim double Eisenstein series,' Res. Number Theory 6 (2020), art. 33 (20 pp).
H. Bachmann, `Modular forms and q-analogues of modified double zeta values,' Abh. Math. Semin. Univ. Hambg. 90 (2020), 201-213; preprint 1808.09674[NT].
Z. Wojtkowiak, `A weak Euler formula for l-adic Galois double zeta values,' Math. J. Okayama Univ. 63 (2021), 87-105; preprint 1811.05747[NT].
T. Nakamura, `Symmetric Tornheim double zeta functions,' Abh. Math. Semin. Univ. Hambg. 91 (2021), 5-14.
J. Li and F. Liu, `Motivic double zeta values of odd weight,' Manuscripta Math. 166 (2021), 19-36; preprint 1710.02244[NT].
K. Dilcher, `Analytic continuation of character and alternating Tornheim zeta functions,' Amer. Math. Monthly 128 (2021), 780-795.
A. Banerjee, T. M. Minamide, and Y. Tanigawa, `Mean square of double zeta-function,' Tokyo J. Math. 44 (2021), 83-101.
M Cenkci and A. Ünal, `A two-variable Dirichlet series and its applications, Quaest. Math. 44 (2021), 1661-1679.
S. Kadota, T. Okamoto, M. Ono, and K. Tasaka, `On a unified double zeta function of Mordell-Tornheim type,' Lith. Math. J. 62 (2022), 207-217; preprint 2104.14794[NT].
D. M. Bradley, `A signed analog of Euler's reduction formula for the double zeta function,' preprint 0707.4486[CA].
G. Bastien, `Elementary methods for evaluating Jordan's sums and analogous Euler's type sums and for setting a sigma sum theorem,' preprint 1301.7662[NT].
K. Adegoke, `On generalized harmonic numbers, Tornheim double series and linear Euler sums,' preprint 1511.03079[NT].
D. Ma, `Connections between double zeta values relative to μ_N, Hecke operators T_N, and newforms of level Γ₀(N) for N=2,3,' preprint 1511.06102[NT].
W. Yang, `Double zeta values and Picard-Fuchs equation,' preprint 1910.09576[NT].
M. Hirose, `Modular phenomena for regularized double zeta values,' preprint 2003.05236[NT].
M. Murahara and T. Nakamura, `On a basis for Euler-Zagier double zeta functions with non-positive components,' preprint 2005.09852[NT].
T. Nakamura, `Rapidly convergent series representations of symmetric Tornheim double zeta functions,' preprint 2103.16873[NT].
Y. Ma and L-P. Teo, `On Zagier's conjecture about the inverse of a matrix related to double zeta values,' preprint 2106.15260[NT].
J. Quan, X. Wang, X. Wei, and C. Xu, `Parametric Euler sums of harmonic numbers,' preprint 2203.10728[NT].
Y. Toma, `Mean value theorems for the Apostol-Vu double zeta-function and its application,' preprint 2204.02012[NT].
H. Hirose, `Colored double zeta values and modular forms of general level, preprint 2205.08507[NT].

B. TRIPLE HARMONIC SERIES

R. Sitaramachandrarao and M. V. Subbarao, `Transformation formulae for multiple series,' Pacific J. Math. 113 (1984), 471-479.
C. Markett, `Triple sums and the Riemann zeta function,' J. Number Theory 48 (1994), 113-132.
J. M. Borwein and R. Girgensohn, `Evaluation of triple Euler sums,' with appendix `Euler sums in quantum field theory' by D. J. Broadhurst, Electronic J. Combinatorics 3 (1996), R23 (27 pp).
M. E. Hoffman and C. Moen, `Sums of triple harmonic series,' J. Number Theory 60 (1996), 329-331.
A. Panholzer and H. Prodinger, `Computer-free evaluation of an infinite double sum via Euler sums,' Sém. Lothar. Combin. 55 (2005), art. B55a (3 pp).
K. Matsumoto, T. Nakamura, and H. Tsumura, `Functional relations and special values of Mordell-Tornheim triple zeta and L-functions,' Proc. Amer. Math. Soc. 136 (2008), 2135-2145.
K. Matsumoto, T. Nakamura, H. Ochiai, and H. Tsumura, `On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions,' Acta Arithmetica 132 (2008), 99-125.
Y. L. Ong, M. Eie, and W-C. Liaw, `Explicit evaluation of triple Euler sums,' Int. J. Number Theory 4 (2008), 437-451.
I. Kiuchi and Y. Tanigawa, `Bounds for triple zeta functions,' Indag. Math. (N. S.) 19 (2008), 97-114.
T. Okamoto, `On alternating analogues of the Mordell-Tornheim triple zeta values,' J. Ramanujan Math. Soc. 28 (2013), 247-269.
T. Machide, `Extended double shuffle relations and the generating functions of triple zeta values of any fixed weight,' Kyushu J. Math.67 (2013), 281-307.
M. Eie and F-Y. Yang, `Weighted sum formulas from shuffle products of multiples of Riemann zeta values,' J. Number Theory 147 (2015), 749-765.
D. Ma and K. Tasaka, `Relationships between multiple zeta values of depth 2 and 3 and period polynomials,' Isr. J. Math. 242 (2021), 359-400; preprint 1707.08178[NT].
J. Li, `Remark on a symmetric zeta function,' preprint 2110.09652[NT].

C. MULTIPLE HARMONIC SERIES/MULTIPLE ZETA VALUES

P. L. Butzer, C. Markett, and M. Schmidt, `Stirling numbers, central factorial numbers, and representations of the Riemann zeta function,' Results Math. 19 (1991), 257-274.
M. E. Hoffman, `Multiple harmonic series,' Pacific J. Math. 152 (1992), 275-290.
D. Zagier, `Values of zeta functions and their applications,' in First European Congress of Mathematics (Paris, 1992), Vol. II, A. Joseph et. al. (eds.), Birkhäuser, Basel, 1994, pp. 497-512.
T. Q. T. Le and J. Murakami, `Kontsevich's integral for the Homfly polynomial and relations between values of the multiple zeta functions,' Topology Appl. 62 (1995), 193-206.
T. Q. T. Le and J. Murakami, `Kontsevich's integral for the Kauffman polynomial,' Nagoya Math. J. 142 (1996), 39-65.
A. Granville, `A decomposition of Riemann's zeta-function,' in Analytic Number Theory, Y. Motohashi (ed.), London Math. Soc. Lecture Note Series 247, Cambridge University Press, Cambridge, 1997, pp. 95-101.
D. J. Broadhurst and D. Kreimer, `Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops,' Physics Lett. B 393 (1997), 403-412.
M. E. Hoffman, `The algebra of multiple harmonic series,' J. Algebra 194 (1997), 477-495.
R. E. Crandall, `Fast evaluation of multiple zeta sums,' Math. Comp. 67 (1998), 1163-1172.
J. M. Borwein, D. M. Bradley, D. J. Broadhurst, and P. Lisoněk, `Combinatorial aspects of multiple zeta values,' Electronic J. Combinatorics 5 (1998), R38 (12 pp).
V. Hoang Ngoc Minh, M. Petitot, and J. Van Der Hoeven, `Computation of the monodromy of generalized polylogarithms,' Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation (Rostock), ACM, New York, 1998, pp. 276-283.
Y. Ohno, `A generalization of the duality and sum formulas on the multiple zeta values,' J. Number Theory 74 (1999), 39-43.
T. Arakawa and M. Kaneko, `Multiple zeta values, poly-Bernoulli numbers, and related zeta functions,' Nagoya Math. J. 153 (1999), 189-209.
T. Takamuki, `The Kontsevich invariant and relations of multiple zeta values,' Kobe J. Math. 16 (1999), 27-43.
V. Hoang Ngoc Minh, G. Jacob, M. Petitot, and N. E. Oussous, `Aspects combinatoires des polylogarithms et des sommes d'Euler-Zagier,' Sém. Lothar. Combin. 43 (1999), art. B43e (29 pp).
J. Zhao, `Analytic continuation of multiple zeta functions,' Proc. Amer. Math. Soc. 128 (2000), 1275-1283.
V. Hoang Ngoc Minh and M. Petitot, `Lyndon words, polylogarithms, and the Riemann ζ function,' Discrete Math. 217 (2000), 273-292.
M. Waldschmidt, `Valeurs zêta multiples. Une introduction,' J. Théor. Nombres Bordeaux 12 (2000), 581-595.
M. Kontsevich and D. Zagier, `Periods,' in Mathematics Unlimited--2001 and Beyond,, B. Engquist and W. Schmid (eds.), Springer, Berlin, 2001, pp. 771-808.
S. Akiyama, S. Egami, and Y. Tanigawa, `Analytic continuation of multiple zeta-functions and their values at non-positive integers,' Acta Arithmetica 98 (2001), 107-116.
K. Ihara and T. Takamuki, `The quantum g2 invariant and relations of multiple zeta values,' J. Knot Theory Ramifications 10 (2001), 983-997.
S. Akiyama and Y. Tanigawa, `Multiple zeta values at non-positive integers,' Ramanujan J. 5 (2001), 327-351.
Y. Ohno and D. Zagier, `Multiple zeta values of fixed weight, depth, and height,' Indag. Math. (N. S.) 12 (2001), 483-487.
D. Bowman and D. M. Bradley, `The algebra and combinatorics of shuffles and multiple zeta values,' J. Combin. Theory Ser. A 97 (2002), 43-61.
M. E. Hoffman, `Periods of mirrors and multiple zeta values,' Proc. Amer. Math. Soc. 130 (2002), 971-974.
T. Terasoma, `Selberg integrals and multiple zeta values,' Compos. Math. 133 (2002), 1-24.
P. Cartier, `Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents,' Astérisque 282 (2002), 137-173 (Sém. Bourbaki no. 885).
U. Müller and C. Schubert, `A quantum field theoretical representation of Euler-Zagier sums,' Internat. J. Math. Math. Sci. 31 (2002), 127-148.
S. Egami and K. Matsumoto, `Asymptotic expansions of multiple zeta functions and power mean values of Hurwitz zeta functions,' J. London Math. Soc. (2) 66 (2002), 41-60.
T. Terasoma, `Mixed Tate motives and multiple zeta values,' Invent. Math. 149 (2002), 339-369; preprint AG/0104231.
S. Fischler, `Formes linéaires en polyzêtas et intégrales multiples,' C. R. Math. Acad. Sci. Paris, Ser. I 335 (2002), 1-4.
K. Matsumoto, `On the analytic continuation of various multiple-zeta functions,' in Number Theory for the Millennium (Urbana, 2000), Vol. II, M. A. Bennett et. al. (eds.), A. K. Peters, Natick, MA, 2002, pp. 417-440.
K. Matsumoto, `The analytic continuation and the asymptotic behavior of certain multiple zeta-functions II', in Analytic and Probabilistic Methods in Number Theory (Palanga, 2001), A. Dubickas et. al. (eds.), TEV, Vilnius, Lithuania, 2002, pp. 188-194.
K. Matsumoto, `The analytic continuation and the asymptotic behavior of certain multiple zeta-functions I', J. Number Theory 101 (2003), 223-243.
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M. Hirose, H. Murahara, and T. Onozuka, `Q-linear relations of specific families of multiple zeta values and the linear part of Kawashima's relation,' Manuscripta Math. 164 (2021), 455-465; preprint 1903.04140[NT].
E. Rowland, R. Yassawi, and C. Krattenthaler, `Lucas congruences for the Apéry numbers modulo p²,' Integers 21 (2021), #A20 (15 pp).
P. Akhilesh, `Multiple zeta values and multiple Apéry-like sums,' J. Number Theory 226 (2021), 72-138; preprint 1912.05204[NT].
M. Kaneko, C. Xu, and S. Yamamoto, `A generalized regularization theorem and Kawashima's relation for multiple zeta values,' J. Algebra 580 (2021), 247-263; preprint 2011.14338[NT].
M. E. Hoffman and M. Kuba, `Logarithmic integrals, zeta values, and tiered binomial coefficients,' Monatsh. Math. 195 (2021), 119-154; preprint 1906.08347[CO].
F. C. S. Brown, `Depth-graded motivic multiple zeta values,' Compos. Math. 157 (2021), 529-572; preprint 1301.3053[NT].
K. Fujita and Y. Komori, `A congruence between symmetric multiple zeta-star values and multiple zeta-star values,' Kyushu J. Math. 75 (2021), 149-167.
C. Xu, `Explicit relations between multiple zeta values and related variants,' Adv. in Appl. Math. 130 (2021), art. 102245 (26 pp); preprint 2012.02588[NT].
Y. Komori, `Finite multiple zeta values, symmetric multiple zeta values,and unified multiple zeta values,' Tohoku Math. J. (2)73 (2021), 221-255.
C. Xu, `Duality formulas for Arakawa-Kaneko zeta values and related variants,' Bull. Malays. Math. Sci. Soc. 44 (2021), 3001-3018.
B. Enriquez and H. Furusho, `The Betti side of the double shuffle theory I. The harmonic coproducts,' Selecta Math. (N.S.) 27 (2021), art. 79; preprint 1803.10151[AG].
K. Matsumoto and M. Nakasuji, `Expressions of Schur multiple zeta-functions of anti-hook type by zeta-functions of root systems,' Publ. Math. Debrecen 98 (2021), 345-377; preprint 2002.01676[NT].
K-W. Chen and M. Eie, `Gamma functions and sum formulas for multiple zeta values,' J. Ramanujan Math. Soc. 36 (2021), 93-107.
S. Charlton, `The alternating block decomposition of iterated integrals, and cyclic insertion on multiple zeta values,' Quarterly J. Math. 72 (2021), 975-1028; preprint 1703.03784[NT].
T. Wakhare and C. Vignat, `Structural properties of multiple zeta values,' Int. J. Number Theory 17 (2021), 1873-1897; preprint 1809.07492[NT].
K. Onodera, `On multiple Hurwitz zeta function of Mordell-Tornheim type,' Int. J. Number Theory 17 (2021), 2327-2360.
M. Hirose, H. Murahara, and M. Ono, `On variants of symmetric multiple zeta-star values and the cyclic sum formula,' Ramanujan J. 56 (2021), 467-489; preprint 2001.03832[NT].
H. Bachmann, Y. Takeyama, and K. Tasaka, `Finite and symmetric Mordell-Tornheim multiple zeta values,' J. Math. Soc. Japan 73 (2021), 1129-1158; preprint 2001.10694[NT].
M. Hirose, N. Sato, and S-I. Seki, `The connector for the double Ohno relation,' Acta Arith. 201 (2021), 109-118.
J. Quan, `Some results on q-multiple harmonic sums,' Filomat 35:2 (2021), 667-677.
D. Essouabri and K. Matsumoto, `Values of multiple zeta-functions with polynomial denominators at non-positive integers,' Internat. J. Math. 32 (2021), art. 2159938; preprint 1908.09248[NT].
N. Komiyama, `On shuffle-type functional relations of desingularized multiple zeta functions,' J. Number Theory 231 (2022), 120-138; preprint 2002.09486[NT].
B. Saha, `Multiple Stieltjes constants and Laurent type expansion of the multiple zeta functions at integer points,' Selecta Math. (N. S.) 28 (2022), art. 6 (41 pp.); preprint 1902.04389[NT].
K. Tasaka, `Note on totally odd multiple zeta values,' Math. J. Okayama Univ. 64 (2022), 63-73; preprint.
D. K. Sahoo and G. K. Viswanadham, `An identity involving weighted and desingularized multiple zeta functions,' Acta Arith. 202 (2022), 195-202.
R. E. Haddad, `A generalization of multiple zeta values. Part 1: Recurrent sums,' Notes Number Theory Discrete Math. 28 (2022), 167-199.
R. E. Haddad, `A generalization of multiple zeta values. Part 2: Multiple sums,' Notes Number Theory Discrete Math. 28 (2022), 200-233.
A. Keilthy, `Motivic multiple zeta values and the block filtration,' J. Number Theory 238 (2022), 883-919; preprint 2006.03003[NT].
M. Hirose, H. Murahara, and M. Ono, `Ohno-type relation for interpolated multiple zeta values,' J. Number Theory 328 (2022), 710-730; preprint 2103.14851[NT]
K. Matsumoto, T. Matsusaka, and I. Tanackov, `On the behavior of multiple zeta-functions with identical arguments on the real line,' J. Number Theory 239 (2022), 151-182; preprint 2012.01720[NT].
F. Chapoton, `Zinbiel algebras and multiple zeta values,' Doc. Math. 27 (2022), 519-533; preprint 2109.00241[NT].
C. Lupu, `Another look at Zagier's formula for multiple zeta values involving Hoffman elements,' Math. Z. 301 (2022), 3127-3140; preprint 2011.11718[NT].
M. Nakasuji and W. Takeda, `The Pieri formula for hook type Schur multiple zeta functions,' J. Combin. Theory Ser. A 191 (2022), no. 105642 (31 pp); preprint 2105.12418[NT]
Z-h. Li, `Algebraic relations of interpolated multiple zeta values,' J. Number Theory 240 (2022), 439-470; preprint 1904.09887[NT].
J. Okuda and K. Ueno, `New approach to Ohno relations for multiple zeta values,' preprint NT/0106148.
S. Kitani, E. Sawada, and K. Ueno, `Finite automata and relations of multiple zeta values,' preprint NT/0403458.
S. A. Zlobin, `A certain integral over a triangle,' preprint NT/0511239.
S. A. Zlobin, `A note on arithmetic properties of multiple zeta values,' preprint NT/0501151.
O. Mathieu, `On a symmetric space attached to polyzeta values,' preprint 0810.0396[NT].
K. Imatomi, T. Tanaka, K. Tasaka, and N. Wakabayashi, `On some combinations of multiple zeta-star values,' preprint 0912.1951[NT].
J. Kuipers and J. A. M. Vermaseren, `About a conjectured basis for multiple zeta values,' preprint 1105.1884[math-ph].
M. Igarashi, `On generalizations of the sum formula for multiple zeta values,' preprint 1110.4875[NT].
J. Merker, `Multizeta calculus I,' preprint 1208.5643[NT].
T. Machide, `A parameterized generalization of the sum formula for quadruple zeta values,' preprint 1210.8005[NT].
T. Terasoma, `Brown-Zagier relation for associators,' preprint 1301.7474[NT].
T. Tanaka, `Restricted sum formula and derivation relation for multiple zeta values,' preprint 1303.0398[NT].
H. Bachmann and U. Kühn, `A short note on a conjecture of Okounkov about a q-analogue of multiple zeta functions,' preprint 1407.6796[NT].
J. Alm, Formal weights in Kontsevich's formality construction and multiple zeta values,' preprint 1410.8377[QA].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - II-1: Standard algebraic relations of prime weighted multiple harmonic sums and adjoint multiple zeta values,' preprint 1412.5099[NT].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - I-2: Indirect solution of the equation of horizontality of Frobenius,' preprint 1501.04893[NT].
A. Chatzistamatiou, `On the integrality of p-adic iterated integrals,' preprint 1501.05760[NT].
H. Furusho, `On relations among multiple zeta values obtained in knot theory,' preprint 1501.06638[QA].
T. Machide, `Use of the generating function to generalize the sum formula for quadruple zeta values,' preprint 1503.01194[NT].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - I-1: Direct solution of the equation of horizontality of Frobenius,' preprint 1503.08756[NT].
W. Zudilin, `On a family of polynomials related to ζ(2,1)=ζ(3),' preprint 1504.07696[NT].
M. Dotzel and I. Horozov, `Shuffle product for multiple Dedekind zeta values over imaginary quadratic fields,' preprint 1509.08400[NT].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - II-2: From algebraic relations of multiple harmonic sums to those of cyclotomic p-adic multiple zeta values,' preprint 1601.01158[NT].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - II-3: Sequences of multiple harmonic sums viewed as periods,' preprint 1601.01159[NT].
A. Vieru, `Analytic renormalization of multiple zeta values. Geometry and combinatorics of generalized Euler reflection formula for MZV,' preprint 1601.04703[NT].
S. Stieberger, `Periods and superstring amplitudes,' preprint 1605.03630[hep-th].
S. Yamamoto, `Multiple zeta values of Kaneko-Tsumura type and their values at positive integers,' preprint 1607.01978[NT].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - I-3: The number of iterations of Frobenius viewed as a variable,' preprint 1610.09107[NT].
S. Yamamoto, `A note on Kawashima functions,' preprint 1702.01377[NT].
K-W. Chen, `Multinomial sum formulas of multiple zeta values,' preprint 1704.05636[NT].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - III-2: Around the nonvanishing of multiple harmonic sums,' preprint 1707.01924[NT].
J. I. Burgos Gil and J. Fresán, Multiple Zeta Values: From Numbers to Motives, to appear.
C. Dietze, C. Manai, C. Nöbel, and F. Wagner, `Totally odd depth-graded multiple zeta values and period polynomials,' preprint 1708.07210[NT].
D. Jarossay, `An explicit theory of π₁^un,crys(P¹-{0,μ_N, ∞}) - V-1: The Frobenius extended to π₁^un,DR(P¹-{0,μ_p^αN,∞}),' preprint 1708.08009[NT].
F. C. S. Brown, `Anatomy of an associator,' preprint 1709.02765[QA].
D. Jarossay, p-Adic multiple zeta values at roots of unity and p-adic pro-unipotent actions - IV-1: p-adic multiple zeta values at roots of unity extended to sequences of integers with any sign,' preprint 1712.09976[NT].
M. Hirose, K. Imatomi, H. Murahara, and S. Saito, `Ohno-type relations for classical and finite multiple zeta-star values,' preprint 1806.09299[NT].
Kh. Hessami Pilehrood and T. Hessami Pilehrood, Multiple zeta-star values on 3-2-1 indices,' preprint 1806.10510[NT].
H. Murahara, `An algebraic proof of the weighted sum formula for finite and symmetric multiple zeta(-star) values,' preprint 1808.01430[NT].
B. Enriquez and H. Furusho, `The Betti side of the double shuffle theory II. Double shuffle relations for associators,' preprint 1807.07786[AG].
H. Hirose, H. Murahara, and T. Onozuka, `Sum formula for multiple zeta function,' preprint 1808.01559[NT].
Y. Komori, K. Matsumoto, and H. Tsumura, `An overview and supplements to the theory of functional relations for zeta-functions of root systems,' preprint 1809.01815[NT].
X. Ai, Generalized multiple zeta values over number fields I,' preprint 1809.07370[NT].
Y. Horikawa, H. Murahara, and K. Oyama, `A note on derivation relations for multiple zeta values and finite multiple zeta values,' preprint 1809.08389[NT].
K-W. Chen and M. Eie, `Some special Euler sums and ζ^☆(r+2,{2}ⁿ),' preprint 1810.11795[NT].
N. Glazunov, `(p-Adic) L-functions and (p-adic) (multiple) zeta values,' preprint 1901.01957[NT].
B. Sadaoui, `Special values of generalized multiple Hurwitz zeta functions at non-positive integers,' preprint 1902.06763[NT].
M. Hirose, H. Murahara, and S. Saito, `Generating functions for Ohno-type sums of finite and symmetric multiple zeta-star values,' preprint 1905.04875[NT].
M. Maassarani, `Bigraded Lie algebras related to MZVs,' preprint 1907.07200[NT].
B. Enriquez and H. Furusho, `The Betti side of the double shuffle theory III. Bitorsor structures,' preprint 1908.00444[AG].
M. DeFranco, `On the multiple zeta values ζ({2}^k),' preprint 1911.07129[NT].
T. Hoshi, `On values of zeta functions of Arakawa-Kaneko type,' preprint 2003.04634[NT].
H. Murahara and T. Onozuka, `Cyclic relation for multiple zeta function,' preprint 2003.08068[NT].
J. Li, `Iterated integrals, multiple zeta values, and Selberg integrals,' preprint 2007.00172[NT].
H. Murahara and T. Tanaka, `Algebraic aspects of rooted tree maps,' preprint 2009.05238[NT].
A. Saad, `Multiple zeta values and iterated Eisenstein integrals,' preprint 2009.09885[NT].
M. Hirose, H. Murahara, and S. Saito, `Generating functions for sums of polynomial multiple zeta values,' preprint 2011.04220[NT].
N. Markarian, `On algebra of big zeta values,' preprint 2011.04944[NT].
H. Murahara, `A note on Ohno sums for multiple zeta values,' preprint 2102.12177[NT].
M. Ono, K. Sakurada, and S-I. Seki, `A note on ℱ_n-multiple zeta values,' preprint 2103.03470[NT]
N. Komiyama, `Relationship between renormalized values of shuffle type and of harmonic type of multiple zeta functions,' preprint 2104.00153[NT]
M. Hirose, H. Murahara, and S. Saito, `Ohno relation for regularized multiple zeta values,' preprint 2105.09631[NT]
M. Ono, `t-Adic symmetrization map on harmonic algebra,' preprint 2106.03682[NT]
H. Bachmann, `q-Analogues of multiple zeta values and the formal double Eisestein space,' preprint 2108.08634[NT].
F. Chapoton, `Multiple T-values with one parameter,' preprint 2108.08534[NT].
C. Dupont, `Valeurs zêta multiples,' preprint 2109.01699[NT].
M. Nakasuji and Y. Ohno, `Duality formula and its generalization for Schur multiple zeta functions,' preprint 2109.14362[NT].
K. W. Chen and M. Eie, `On the convolutions of sums of multiple zeta(-star) values of of height one,' preprint 2110.00231[NT].
N. Komiyama, `On properties of adari(pal) and ganit(pic),' preprint 2110.04834[QA].
B. Brindle, `A unified approach to qMZVs,' preprint 2111.00051[NT].
B. Brindle, `Proving dualities for qMZVs with connected sums,' preprint 2111.00058[NT].
M. Kobayashi, `From Basel problem to multiple zeta values,' preprint 2112.03361[NT].
S. Chavan, M. Kobayashi, and J. Layja, `Integral evaluation of odd Euler sums, multiple t-value t(3,2,...,2), and multiple zeta value ζ(3,2,...,2),' preprint 2111.07097[NT].
J. Li, `A continuous version of multiple zeta functions,' preprint 2111.15062[NT].
P. Li, `The complex genera, symmetric functions, and multiple zeta values,' preprint 2112.01192[DG].
J. A. Arciniega-Nevárez, M. Berghoff, and E. R. Dolores-Cuenca, `Virtual posets, shuffle algebras, and associators,' preprint 2112.06228[QA].
M. Nakasuji and W. Takeda, `Shuffle product formula of the Schur multiple zeta values of hook type,' preprint 2201.01402[NT].
L. Lai, C. Lupu, and D. Orr, `Elementary proofs of Zagier's formula for multiple zeta values and its odd variant,' preprint 2201.09262[NT].
K-W. Chen and M. Eie, `On three general forms of multiple zeta(-star) values,' preprint 2202.03839[NT].
A. Keilthy, `A generalization of quasi-shuffle algebras and an application to multiple zeta values,' preprint 2202.04739[NT].
M. Hirose, H. Murakawa, and S. Saito, `t-Adic multiple zeta values for indices in which 1 and 3 appear alternately,' preprint 2203.07701[NT].
H. Bachmann and J. van Ittersum, `Partitions, multiple zeta values, and the q-bracket,' preprint 2203.09165[NT].
K-W. Chen and M. Eie, `Weighted sum formulas from shuffle products of multiple zeta-star values,' preprint 2203.14030[NT].
H. Bachmann and A. Burmester, `Combinatorial multiple Eisenstein series,' preprint 2203.17074[NT].
M. Nakasuji, Y. Ohno, and W. Takeda, `An interpolation of the generalized duality formula for the Schur multiple zeta values to complex functions,' preprint 2204.04839[NT].
T. Machide, `Computations about formal multiple zeta spaces defined by binary extended double shuffle relations,' preprint 2205.13751[NT].
M. Igarashi, `Note on cyclic sum of certain parametrized multiple series,' preprint 2206.01190[NT].
M. Hirose and N. Sato, `Block shuffle identities for multiple zeta values,' preprint 2206.03458[NT].
A. Kimura, `Intersection of duality and derivation relations for multiple zeta values,' preprint 2208.08556[NT].

D. MULTIPLE ZETA VALUES OVER FUNCTION FIELDS

D. S. Thakur, Function Field Arithmetic, World Scientific, Singapore, 2004.
R. Masri, `Multiple zeta values over global function fields,' in Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory (Bretton Woods, 2005), S. Friedberg et. al. (eds.), Proc. Symp. Pure Math. 75, Amer. Math. Soc., Providence, RI, 2006, pp. 157-175.
G. W. Anderson and D. S. Thakur, `Multizeta values for F_q[t], their period interpretation, and relations between them,' Int. Math. Res. Notices 2009, 2038-2055; preprint 0902.1180[NT].
D. S. Thakur, `Relations between multizeta values for F_q[t]', Int. Math. Res. Notices 2009, 2318-2346.
D. S. Thakur, `Power sums with applications to multizeta and zeta zero distribution for F_q[t]', Finite Fields Appl. 15 (2009), 534-552.
J. A. Lara Rodríguez, `Some conjectures and results about multizeta values over F_q[t]', J. Number Theory 130 (2010), 1013-1023.
D. S. Thakur, `Shuffle relations for function field multiple zeta values,' Int. Math. Res. Notices 2010, 1973-1980.
J. A. Lara Rodríguez, `Relations between multizeta values in characteristic p,' J. Number Theory 131 (2011), 2081-2099.
J. A. Lara Rodríguez, `Special relations between multizeta values and parity results,' J. Ramanujan Math. Soc. 27 (2012), 275-293; preprint 1108.4726[NT].
Chieh-Yu Chang, `Linear independence of monomials of multizeta values in positive characteristic,' Compos. Math. 150 (2014), 1789-1808; preprint 1207.2326[NT].
J. A. Lara Rodríguez and D. S. Thakur, Zeta-like multizeta values for F_q[t],' Indian J. Pure Appl. Math. 45 (2014), 787-801; preprint 1312.4928[NT].
Chieh-Yu Chang, `On characteristic p multizeta values,' in Algebraic Number Theory and Related Topics 2012, A. Shiho et. al. (eds.), RIMS Kōkyūroku Bessatsu B51 (2014), pp. 177-202.
D. S. Thakur, `Arithmetic of gamma, zeta and multizeta values for function fields,' in Arithmetic Geometry over Function Fields , F. Bars et. al. (eds.), Birkhäuser, Basel, 2014, pp. 197-279.
H-J. Chen, `On shuffle of double zeta values over F_q[t],' J. Number Theory 148 (2015), 153-163.
Y. Mishiba, `Algebraic independence of the Carlitz period and the positive characteristic multizeta values at n and (n,n),' Proc. Amer. Math. Soc. 143 (2015), 3753-3763; preprint 1307.3725[NT].
J. A. Lara Rodríguez and D. S. Thakur, `Multizeta shuffle relations for function fields with non rational infinite place,' Finite Fields Appl. 37 (2016), 344-356.
Y-L. Kuan and Y-H. Lin, `Criterion for deciding zeta-like multizeta values in positive characteristic,' Experiment. Math. 25 (2016), 246-256.
F. Pellarin, `A note on multiple zeta values in Tate algebras,' Riv. Mat. Univ. Parma 7 (2016), 71-100; preprint 1601.07348[NT].
Chieh-Yu Chang, `Linear relations among double zeta values in positive characteristic,' Cambridge J. Math. 4 (2016), 289-331; preprint 1510.06519[NT].
Y. Mishiba, `On algebraic independence of certain multizeta values in characteristic p,' J. Number Theory 173 (2017), 512-528; preprint 1401.3628[NT].
D. S. Thakur, `Multizeta values for function fields: a survey,' J. Théor. Nombres Bordeaux 29 (2017), 997-1023.
F. Pellarin, `A sum-shuffle formula for zeta values in Tate algebras,' J. Théor. Nombres Bordeaux 29 (2017), 1025-1048; preprint 1609.08873[NT].
Chieh-Yu Chang and Y. Mishiba, `On finite Carlitz multiple polylogarithms,' J. Théor. Nombres Bordeaux 29 (2017), 1049-1058; preprint 1611.02822[NT].
H-J. Chen, `Anderson-Thakur polynomials and multizeta values in positive characteristic,' Asian J. Math. 21 (2017), 1135-1152; preprint 1506.06463[NT].
H-J. Chen and Y-L. Kuan, `On depth 2 zeta-like families,' J. Number Theory 184 (2018), 411-427.
G. Todd, `A conjectural characterization of F_q[t]-linear relations between multizeta values,' J. Number Theory 187 (2018), 264-287.
R. Harada, `On Lara Rodriguez' full conjecture for double zeta values in function fields,' Int. J. Number Theory 14 (2018), 1081-1092; preprint 1701.04552[NT].
Chieh-Yu Chang, M. A. Papanikolas, and J. Yu, `An effective criterion for Eulerian multizeta values in positive characteristic,' J. Eur. Math. Soc. 21 (2019), 405-440; preprint 1411.0124[NT].
Chieh-Yu Chang and Y. Mishiba, `On multiple polylogarithms in characteristic p: v-adic vanishing versus ∞-adic Eulerianness,' Int. Math. Res. Notices 2019, 923-947; preprint 1511.03490[NT].
D. Basak, N. Degré-Pelletier, and M. N. Lalín, `Multiple zeta functions and polylogarithms over global function fields,' J. Théor. Nombres Bordeaux 32 (2020), 403-439.
O. Gezmiş, `Deformation of multiple zeta values and their logarithmic interpretation in positive characteristic,' Doc. Math. 25 (2020), 2355-2412; preprint 1910.02805[NT].
D. S. Thakur, `Multizeta in function field arithmetic,' in t-Motives: Hodge Structures, Transcendence and Other Motivic Aspects, G. Böckle et. al. (eds.), EMS Ser. Congr. Rep. 16, EMS Publishing House, Berlin, 2020, pp. 441-452.
Chieh-Yu Chang and Y. Mishiba, `On a conjecture of Furusho over function fields,' Invent. Math. 223 (2021), 49-102; preprint 1710.10849[NT].
T. Ngo Dac, `On Zagier-Hoffman's conjectures in positive characteristic,' Ann. of Math. (2) 194 (2021), 361-392.
R. Harada, `Alternating multizeta values in positive characteristic,' Math. Z. 298 (2021), 1263-1291; preprint 1909.03849[NT].
R. Harada and Y-T. Chen, `On lower bounds of the dimensions of multizeta values in positive characteristic,' Doc. Math. 26 (2021), 537-559.
Chieh-Yu Chang, N. Green, and Y. Mishiba, `Taylor coefficients of Anderson-Thakur series and explicit formulae,' Math. Ann. 379 (2021), 1425-1474; preprint 1902.06879[NT].
F. Pellarin and R. Perkins, `On twisted A-harmonic sums and Carlitz finite zeta values,' J. Number Theory 232 (2022), 355-378.
W-C. Huang, `A t-motivic interpretation of shuffle relations for multizeta values,' J. Number Theory 232 (2022), 379-405; preprint 1904.02248[NT].
Q. Shen, `Zero distribution of v-adic multiple zeta values over F_q(t),' Int. J. Number Theory 18 (2022), 131-139; preprint 1912.10365[NT].
S. Shi, `Vanishing of multiple zeta values over F_q[t] at negative integers,' Canad. Math. Bull 65 (2022), 9-29; preprint 2003.12242[NT].
H. H. Le and T. Ngo Dac, `Zeta-like multiple zeta values in positive characteristic,' Math. Z. 301 (2022), 2037-2057.
K. Joshi, `The t-motivic mixed Carlitz zeta category and Carlitz-Thakur multi-zeta values,' preprint 1306.2506[NT].
Y-T. Chen, `Integrality of v-adic multiple zeta values,' preprint 2001.01855[NT].
J. A. Lara Rodríguez and D. S. Thakur, `Zeta-like multizeta values for higher genus curves,' preprint 2003.12910[NT].
Chieh-Yu Chang, Y-T. Chen, and Y. Mishiba, `Algebra structure of multiple zeta values in positive characteristic,' preprint 2007.08264[NT].
N. Green and T. Ngo Dac, `On log-algebraic identities for Anderson t-modules and characteristic p multiple zeta values,' preprint 2007.11060[NT].
O. Gezmiş and F. Pellarin, `Trivial multiple zeta values in Tate algebras,' preprint 2008.07144[NT].
K. Chung, T. Ngo Dac, and F. Pellarin, `Universal families of Eulerian multiple zeta values in positive characteristics,' preprint 2111.06973[NT].
D. Matsuzuki, `On ∞-adic and v-adic multiple zeta functions in positive characteristic,' preprint 2201.12953[NT].
B-H. Im, H. Kim, K. N. Le, T. Ngo Dac, and L. H. Pham, `Zagier-Hoffman's conjectures in positive characteristic,' preprint 2205.07165[NT].
Chieh-Yu Chang, Y-T. Chen, and Y. Mishiba, `On Thakur's basis conjecture for multiple zeta values in positive characteristic,' preprint 2205.09929[NT].
J. A. Lara Rodríguez, `Two term relations between multizeta of depth two for F_q[t],' preprint 2208.06277[NT].

E. ALTERNATING SERIES

D. H. Bailey, J. M. Borwein, and R. Girgensohn, `Experimental evaluation of Euler sums,' Experiment. Math. 3 (1994), 17-30.
D. Borwein, J. M. Borwein, and R. Girgensohn, `Explicit evaluation of Euler sums,' Proc. Edinburgh Math. Soc. 38 (1995), 277-294.
V. Adamchik, `On Stirling numbers and Euler sums,' J. Comp. Appl. Math. 79 (1997), 119-130.
D. J. Broadhurst, J. M. Borwein, and D. M. Bradley, `Evaluation of k-fold Euler/Zagier sums: a compendium of results for arbitrary k,' Electronic J. Combinatorics 4(2) (1997), R5.
Wenchang Chu, `Hypergeometric series and the Riemann zeta function,' Acta Arithmetica 82 (1997), 103-118.
P. Flajolet and B. Salvy, `Euler sums and contour integral representations,' Experiment. Math. 7 (1998), 15-35.
M. Bigotte, G. Jacob, N. E. Oussous, and M. Petitot, `Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables,' Theoret. Comput. Sci. 273 (2002), 271-283.
D. Borwein, J. M. Borwein, and D. M. Bradley, `Parametric Euler sum identities,' J. Math. Anal. Appl. 316 (2006), 328-338.
J. M. Borwein and D. M. Bradley, `Thirty-two Goldbach variations,' Intl. J. Number Theory 2 (2006), 65-103; preprint NT/0502034.
M. N. Lalín, `On a certain combination of colored multizeta values,' J. Ramanujan Math. Soc. 20 (2006), 115-127; preprint NT/0603442.
J-Y. Enjalbert and V. Hoang Ngoc Minh, `Analytic and combinatoric aspects of Hurwitz polyzêtas', J. Théor. Nombres Bordeaux 19 (2007), 595-640.
D-Y. Zheng, `Further summation formulae related to generalized harmonic numbers,' J. Math. Anal. Appl. 335 (2007), 692-706.
R-O. Vîlceanu, `The multiple zeta function and the computation of some integrals in compact form,' An. Univ. Craiova Ser. Mat. Inform. 35 (2008), 182-198.
J. Choi and H. M. Srivastava, `Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals,' Math. Nachr. 282 (2009), 1709-1723.
J. Blümlein, D. J. Broadhurst, and J. A. M. Vermaseren, `The multiple zeta value data mine,' Comput. Phys. Commun. 181 (2010), 582-625; preprint 0907.2557[math-ph].
J. Zhao, `On a conjecture of Borwein, Bradley and Broadhurst,' J. reine angew. Math. 639 (2010), 223-233; cf. preprint 0705.2267[NT].
J. Zhao, `Alternating Euler sums and special values of Witten multiple zeta function attached to so(5),' J. Aust. Math. Soc. 89 (2010), 419-430; preprint 0903.0473[NT].
Z. Shen and T. Cai, `Some identities for alternating multiple zeta values' (Chinese), Acta Math. Sinica (Chin. Ser.) 56 (2013), 441-450.
D. H. Bailey, D. Borwein, and J. M. Borwein, `On Eulerian log-gamma integrals and Tornheim-Witten zeta functions,' Ramanujan J. 36 (2015), 43-68.
J. Zhao, `Restricted sum formula of alternating Euler sums,' Ramanujan J. 36 (2015), 375-401; preprint 1207.5366[NT].
C. Xu, Y. Yang, and J. Zhang, `Explicit evaluation of quadratic Euler sums,' Int. J. Number Theory 13 (2017), 655-672; preprint 1609.04923[NT].
C. Xu, `Identities for the multiple zeta (star) values,' Results Math. 73 (2018), no. 3; preprint 1702.03868[NT].
C. Xu, `Explicit evaluation of harmonic sums,' Commun. Korean Math. Soc. 33 (2018), 13-36; preprint 1612.00388[NT].
L-P. Teo, `Alternating double Euler sums, hypegeometric identities and a theorem of Zagier,' J. Math. Anal. Appl. 462 (2018), 777-800; preprint 1709.01269[CV].
C. Xu, Some evaluation of cubic Euler sums, J. Math. Anal. Appl. 466 (2018), 789-805; preprint 1705.06088[NT].
A. Berglund and J. Bergström, `Hirzebruch L-polynomials and multiple zeta values,' Math. Ann. 372 (2018), 125-137; preprint 1708.05547[AT].
D. Orr, `Generalized log-sine integrals and Bell polynomials,' J. Comput. Appl. Math. 347 (2019), 330-342; preprint 1705.04723[NT].
C. Xu, `Integrals of logarithmic functions and alternating multiple zeta values,' Math. Slovaca 69 (2019), 339-356; preprint 1701.00385[NT].
M. E. Hoffman, `An odd variant of multiple zeta values,' Commun. Number Theory Phys. 13 (2019), 529-567; preprint 1612.05232[NT].
C. Xu and W. Wang, `Explicit formulas of Euler sums via multiple zeta values,' J. Symbolic Comput. 101 (2020), 109-127; preprint 1805.08056[NT].
Z-h. Li and C. Xu, `Weighted sum formulas of multiple t-values with even arguments,' Forum Math. 32 (2020), 965-967. preprint 1908.03200[NT]
C. Xu, `Some results on multiple polyogarithm functions and alternating multiple zeta values,' J. Number Theory 214 (2020), 177-201.
J. Quan, `Alternating double t-values and T-values,' Adv. Difference Equ. 2020:450 (13 pp).
M. E. Hoffman, M. Kuba, M. Levy, and G. Louchard, `An asymptotic series for an integral,' Ramanujan J. 53 (2020), 1-25; preprint 1802.09214[NT].
I. Mező, `Log-sine-polylog integrals and alternating Euler sums,' Acta Math. Hungar. 160 (2020), 45-57.
C. Xu, `Explicit formulas of some mixed Euler sums via alternating multiple zeta values,' Bull. Malays. Math. Sci. Soc. 43 (2020), 3809-3827.
Z. Jin and J. Li, `Motivic multiple zeta values relative to µ₂', Algebra Number Theory 14 (2020), 2685-2712; preprint 1805.02126[NT].
M. Kaneko and H. Tsumura, `On multiple zeta values of level two,' Tsukuba J. Math. 44 (2020), 213-234; preprint 1903.03747[NT].
W. Wang and C. Xu, `Alternating multiple zeta values, and explicit formulas of some Euler-Apéry-type series,' European J. Combin. 93 (2021), art. 103283 (22 pp); preprint 1909.02943[NT].
Y. He and Z. Chen, `Some weighted sum formulas for multiple zeta, Hurwitz zeta, and alternating multiple zeta values,' J. Math. 2021, art. 6672532 (16 pp).
Z. Shen and H. He, `Some identities for multiple alternating zeta values,' J. Number Theory 228 (2021), 8-21.
C. Xu, `Explicit evaluations for several variants of Euler sums,' Rocky Mountain J. Math. 51 (2021), 1089-1106.
C. Xu, `Duality of weighted sum formulas of alternating multiple T-values,' Bull. Korean Math. Soc. 58 (2021), 1261-1278; preprint 2006.02967[NT]
M. Genčev, `A weighted sum formula for alternating zeta-star values,' Mediterr. J. Math. 18 (2021), art. 236 (15 pp).
J. Quan, `Explicit formulas of alternating multiple zeta star values ζ^★(1, {1}_m-1,1) and ζ^★(2,{1}_m-1, 1),' AIMS Mathematics 7(1); 288-293.
Y. Takeyama, `On a weighted sum of multiple T-values of fixed weight and depth,' Bull Aust. Math. Soc. 104 (2021), 398-405; preprint 2012.11063[NT]
C. Xu, `Extensions of Euler-type sums and Ramanujan-type sums,' Kyushu J. Math. 75 (2021), 295-322.
T. Murakami, `On Hoffman's t-values of maximal height and generators of multiple zeta values,' Math. Ann. 382 (2022), 421-458.
C. Xu and J. Zhao, `Variants of multiple zeta values with even and odd summation indices,' Math. Z. 300 (2022), 3109-3142; preprint 2008.13157[NT]
D. J. Broadhurst, `On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory,' preprint hep-th9604128.
D. J. Broadhurst, `Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams,' preprint hep-th9612012.
Z-h. Li, `On harmonic sums and alternating Euler sums,' preprint 1012.5192[NT].
G. Louchard, `Two applications of polylog functions and Euler sums,' preprint 1709.08686[CO].
C. Xu and W. Wang, `Two variants of Euler sums,' preprint 1906.07654[NT].
C. Xu and J. Zhao, `Explicit relations between Kaneko-Yamamoto type multiple zeta values and related variants,' preprint 2008.13163[NT]
W. Wang and C. Xu, `Dirichlet type extensions of Euler sums,' preprint 2009.11704[NT]
S. Berger, A. Chandra, J. Jain, D. Xu, C. Xu, and J. Zhao, `Proof of Kaneko-Tsumura Conjecture on Triple T-values,' preprint 2011.02393[NT]
W. Wang and C. Xu, `On variants of the Euler sums and symmetric extensions of the Kaneko-Tsumura conjecture,' preprint 2108.13204[NT]
C. Xu and J. Zhao, `Apéry-type series and colored multiple zeta values,' preprint 2111.10998[NT]
S. Charlton, `On motivic multiple t values, Saha's basis conjecture, and generators of alternating MZVs,' preprint 2112.14613[NT]
C. Xu and J. Zhao,`Apéry-type series with summation indicies of mixed parities and colored multiple zeta values I,' preprint 2202.06195[NT]
C. Xu and J. Zhao,`Apéry-type series with summation indicies of mixed parities and colored multiple zeta values II,' preprint 2203.00777[NT]
C. Xu and L. Yan, `Parametric Euler T-sums of odd harmonic numbers,' preprint 2203.13996[NT]
S. Charlton and M. E. Hoffman, `Symmetry results for multiple t-values,' preprint 2204.14183[NT]
C. Xu and J. Zhao,`Apéry-type series with summation indicies of mixed parities and colored multiple zeta values III,'preprint 2205.01000[NT]

F. MULTIPLE POLYLOGARITHMS/NESTED SUMS

A. B. Goncharov, `Multiple polylogarithms, cyclotomy, and modular complexes,' Math. Res. Lett. 5 (1998), 497-516.
D. J. Broadhurst, `Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity,' European Phys. J. C (Fields) 8 (1999), 311-333; preprint hep-th9803091.
M. E. Hoffman, `Quasi-shuffle products,' J. Algebraic Combin. 11 (2000), 49-68; preprint QA/9907173.
E. Remiddi and J. A. M. Vermaseren, `Harmonic polylogarithms,' Int. J. Modern Phys. A 15 (2000), 725-754; preprint hep-ph/9905237.
A. B. Goncharov, `The dihedral Lie algebras and Galois symmetries of π₁^(l)( P¹-({0,∞}∪μ_N)),' Duke Math. J. 110 (2001), 397-487; preprint AG/0009121.
M. Yu. Kalmykov and O. Veretin, `Single scale diagrams and multiple binomial sums,' Phys. Lett. B 483 (2000), 315-323; preprint hep-th/0004010.
A. I. Davydychev and M. Yu. Kalmykov, `Some remarks on the ε-expansion of dimensionally regulated Feynman diagrams,' Nuclear Phys. B (Proc. Suppl.) 89 (2000), 283-288; preprint hep-th/0005287.
V. Hoang Ngoc Minh, M. Petitot, J. Van Der Hoeven, `Shuffle algebra and polylogarithms,' Discrete Math. 225 (2000), 217-230.
A. I. Davydychev and M. Yu. Kalmykov, `New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams,' Nuclear Phys. B 605 (2001), 266-318; preprint hep-th/0012189.
J. M. Borwein, D. M. Bradley, D. J. Broadhurst, and P. Lisoněk, `Special values of multidimensional polylogarithms,' Trans. Amer. Math. Soc. 353 (2001), 907-941.
J. M. Borwein, D. J. Broadhurst, and J. Kamnitzer, `Central binomial sums, multiple Clausen values, and zeta values,' Experiment. Math. 10 (2001), 25-34.
V. Hoang Ngoc Minh, G. Jacob, M. Petitot, and N. E. Oussous, `De l'algèbre des ζ de Riemann multivariées à l'algèbre des ζ de Hurwitz multivariées,' Sém. Lothar. Combin. 44 (2001), art. B44i (21 pp).
D. Bowman and D. M. Bradley, `Multiple polylogarithms: a brief survey,' in Conference on q-Series with Applications to Combinatorics, Number Theory, and Physics (Urbana, IL, 2000), B. C. Berndt and K. Ono (eds.), Contemp. Math. 291, Amer. Math. Soc., Providence, RI, 2001, pp. 71-92.
G. Racinet, `Torseurs associés à certaines relations algébriques entre polyzêtas aux racines de l'unité,' C. R. Acad. Sci. Paris Ser. I Math. 333 (2001), 5-10.
G. Racinet, `Algèbre de Lie de valeuers formelles d'hyperlogarithmes aux racines de l'unité' C. R. Acad. Sci. Paris Ser. I Math. 333 (2001), 11-16.
S. Moch, P. Uwer, and S. Weinzierl, `Nested sums, expansion of transcendental functions and multiscale multiloop integrals,' J. Math. Phys. 43 (2002), 3363-3386; preprint hep-ph0110083.
A. B. Goncharov, `Multiple ζ-values, Galois groups, and geometry of modular varieties,' in European Congress of Mathematics (Barcelona, 2000), Vol. I, Progr. Math. 201, Birkhäuser, Basel, 2001, pp. 361-392; preprint AG/0005069.
G. Racinet, `Doubles mélanges des polylogarithmes multiples aux racines de l'unité,' Publ. Math. IHES 95 (2002), 185-231; preprint QA/0202142; English translation (courtesy of D. Moskovich).
M. Waldschmidt, `Multiple polylogarithms: an introduction,' in Number Theory and Discrete Mathematics (Chandigarh, 2000), A. K. Agarwal et. al. (eds.), Birkhäuser, Basel, 2002, pp. 1-12.
S. Akiyama and H. Ishikawa, `On analytic continuation of multiple L-functions and related zeta functions,' in Analytic Number Theory, C. Jia and K. Matsumoto (eds.), Developments in Math. 6, Kluwer, Dordrecht, 2002, pp. 1-16.
M. N. Lalín, `Some examples of Mahler measure as multiple polylogarithms,' J. Number Theory 103 (2003), 85-108.
E. A. Ulanskii, `Identities for generalized polylogarithms' (Russian), Mat. Zametki 73 (2003), 613-624; English translation in Math. Notes 73 (2003), 571-581.
M. Kaneko and T. Arakawa, `On multiple L-values,' J. Math. Soc. Japan 56 (2004), 967-991.
V. Hoang Ngoc Minh, `Shuffle algebra and differential Galois group of colored polylogarithms,' Nuclear Phys. B (Proc. Suppl.) 135 (2004), 220-224.
J. Okuda, `Duality formulas of the special values of multiple polylogarithms,' Bull. London Math. Soc. 37 (2005), 230-242; preprint CA/0307137.
J. Vollinga and S. Weinzierl, `Numerical evaluation of multiple polylogarithms,' Comput. Phys. Commun. 167 (2005), 177-194; preprint hep-ph/0410259.
K. Matsumoto and H. Tsumura, `Generalized multiple Dirichlet series and generalized multiple polylogarithms,' Acta Arithmetica 124 (2006), 139-158.
Q. Wang, `Moduli spaces and multiple polylogarithm motives,' Adv. in Math. 206 (2006), 329-357; preprint AG/0610670.
M. de Crisenoy, `Values at T-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables,' Compos. Math. 142 (2006), 1373-1402.
Yu. I. Manin, `Iterated integrals of modular forms and noncommutative modular symbols,' in Algebraic Geometry and Number Theory, V. Ginzburg (ed.), Progress in Math. 256, Birkhäuser Boston, Boston, 2006, pp. 565-597; preprint AG/0502576.
M. Yu. Kalmykov, B. F. L. Ward and S. Yost, `All order ε-expansion of Gauss hypergeometric functions with integer and half-integer values of parameters,' J. High Energy Phys. (2007), 02#040 (20 pp).
M. Yu. Kalmykov, B. F. L. Ward and S. Yost, `Multiple (inverse) binomial sums of arbitrary weight and depth and the all-order ε-expansion of generalized hypergeometric functions with one half-integer value of parameter,' J. High Energy Phys. (2007), 10#048 (26 pp).
M. Yu. Kalmykov, B. F. L. Ward and S. Yost, `On the all-order ε-expansion of generalized hypergeometric functions with integer values of parameters,' J. High Energy Phys. (2007), 11#009 (12 pp).
J. Zhao, `Analytic continuation of multiple polylogarithms,' Analysis Math. 33 (2007), 301-323; preprint AG/0302054.
H. Tsumura, `On the parity conjecture for multiple L-values of conductor four,' Tokyo J. Math. 30 (2007), 21-40.
J. Sondow and S. A. Zlobin, `Integrals over polytopes, multiple zeta values and polylogarithms, and Euler's constant' (Russian), Mat. Zametki 84 (2008), 606-626; English translation in Math. Notes 84 (2008), 568-583; preprint 0705.0732[NT].
J. Zhao, `Multiple polylogarithm values at roots of unity,' C. R. Math. Acad. Sci. Paris Ser. I 346 (2008), 1029-1032; cf. preprint 0810.1064[NT].
M. de Crisenoy and D. Essouabri, `Relations between values at T-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables,' J. Math. Soc. Japan 60 (2008), 1-16.
N. Kurokawa, M. N. Lalín and H. Ochiai, `Higher Mahler measures and zeta functions,' Acta Arithmetica 135 (2008), 269-297; preprint 0908.0171[NT].
M. Yu. Kalmykov and B. A. Kniehl, `Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters,' Nuclear Phys. B 809 (2009), 365-405; preprint 0807.0567[hep-th].
K. Kimoto and Y. Yamasaki, `A variation of multiple L-values arising from the spectral zeta function of the non-commutative harmonic oscillator,' Proc. Amer. Math. Soc. 137 (2009), 2503-2515.
Y. Yamasaki, `Evaluations of multiple Dirichlet L-values via symmetric functions,' J. Number Theory 129 (2009), 2369-2386; preprint 0712.1639[NT].
T. Mansour, `Identities for sums of a q-analogue of polylogarithm functions,' Lett. Math. Phys. 87 (2009), 1-18.
S. Weinzierl, `Feynman integrals and multiple polylogarithms,' in Renormalization and Galois Theories, A. Connes et. al. (eds.), European Math. Soc., Zürich, 2009, pp. 245-270.
S. Oi, `Gauss hypergeometric functions, multiple polylogarithms, and multiple zeta values,' Publ. Res. Inst. Mat. Sci. 45 (2009), 981-1009; cf. preprint 0810.1829[QA].
J. Zhao, `Standard relations of multiple polylogarithms at roots of unity,' Documenta Math. 15 (2010), 1-34.
A. Zaharescu and M. Zaki, `On the singularities of multiple L-functions,' Cent. Eur. J. Math. 8 (2010), 289-298.
Y. Komori, K. Matsumoto and H. Tsumura, `On multiple Bernoulli polynomials and multiple L-functions of root systems,' Proc. London Math. Soc. (3) 100 (2010), 303-347.
J. Zhao, `Multi-polylogs at twelfth roots of unity and special values of Witten multiple zeta function attached to the exceptional Lie algebra g₂,' J. Algebra Appl. 9 (2010), 327-337; preprint 0904.0888[NT].
M. Yu. Kalmykov and B. A. Kniehl, `"Sixth root of unity" and Feynman diagrams: hypergeometric function approach point of view,' Nuclear Phys. B (Proc. Suppl.) 205-206 (2010), 129-134; preprint 1007.2373[math-ph].
S. Oi and K. Ueno, `Iterated integrals and relations of multiple polylogarithms,' in Representation Theory and Combinatorics, RIMS Kōkyūroku 1689 (2010), pp. 101-116.
Y. Komori, K. Matsumoto, and H. Tsumura, `Multiple Bernoulli polynomials and multiple zeta-functions of root systems,' in Representation Theory and Combinatorics, RIMS Kōkyūroku 1689 (2010), pp. 117-132.
G. Yamashita, `Bounds for the dimensions of p-adic multiple L-value spaces,' Doc. Math., special volume for G. Suslin 60th birthday (2010), 687-723.
Y. Komori, K. Matsumoto, and H. Tsumura, `A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems,' in Infinite Analysis 2010 Developments in Quantum Integrable Systems, A. Kuniba et. al. (eds.), RIMS Kōkyūroku Bessatsu B28 (2011), 99-120.
D. Essouabri, K. Matsumoto, and H. Tsumura, `Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula,' Canad. J. Math. 63 (2011), 241-276.
G. Kawashima, T. Tanaka, and N. Wakabayashi, `Cyclic sum formula for multiple L-values,' J. Algebra 348 (2011), 336-349.
J. M. Borwein and A. Straub, `Special values of generalized log-sine integrals,' ISAAC 2011-Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation (San Jose, June 2011), A. Leykin (ed.), ACM, New York, 2011, pp. 43-50.
J. Zhao and X. Zhou, `Reducibility of signed cyclic sums of Mordell-Tornheim zeta and L-values,' J. Ramanujan Math. Soc. 26 (2011), 383-414; preprint 0902.1262[NT].
B. Enriquez and H. Furusho, `Mixed pentagon, octagon and Broadhurst duality equations,' J. Pure Appl. Algebra 216 (2012), 982-995.
S. Zlobin, `Special values of generalized polylogarithms' (Russian), Fundam. Prikl. Mat. 16 (2010), 63-89; English translation in J. Math. Sci. 182 (2012), 484-504; preprint 0712.1656[NT].
S. Oi and K. Ueno, `KZ equation on the moduli space M_0,5 and the harmonic product of multiple polylogarithms,' Proc. London Math. Soc. (3) 105 (2012), 983-1020; preprint 0910.0718[QA].
J. Enjalbert and V. Hoang Ngoc Minh, `Combinatorial study of colored Hurwitz polyzêtas,' Discrete Math. 312 (2012), 3489-3498; preprint 1206.1216[CO].
H. Furusho, `Geometric interpretation of double shuffle relation for multiple L-values,' in Galois-Teichmüller Theory and Arithmetic Geometry, H. Nakamura et. al. (eds.), Adv. Studies in Pure Math. 68, Math. Soc. Japan, Tokyo, 2012, pp. 163-187.
G. Yamashita, `p-Adic multiple zeta values, p-adic multiple L-values, and motivic Galois groups,' in Galois-Teichmüller Theory and Arithmetic Geometry, H. Nakamura et. al. (eds.), Adv. Studies in Pure Math. 68, Math. Soc. Japan, Tokyo, 2012, pp. 629-658.
M. Zakrzewski, `Asymptotic analysis and special values of generalized multiple zeta values,' in Formal and analytic solutions to differential equations (Będlewo, 2011), W. Balser et. al. (eds.), Banach Center Publications 97, Polish Acad. Sci., Inst. of Mathematics, Warsaw, 2012, pp. 179-190.
J. M. Borwein and A. Straub, `Log-sine evaluations of Mahler measures,' J. Aust. Math. Soc. 92 (2012), 15-36.
P. Borwein, J. M. Borwein, A. Straub, and J. Wan, `Log-sine evaluations of Mahler measures II,' Integers 12a (2012), #A5, 1179-1212.
C. Duhr, H. Gangl, and J. R. Rhodes, `From polygons and symbols to polylogarithmic functions,' J. High Energy Phys. (2012) 10#75 (77 pp).
L. Guo and B. Xie, `Explicit double shuffle relations and a generalization of Euler's decomposition formula,' J. Algebra 380 (2013), 46-77; preprint 0808.2618[NT].
C. Anzai and Y. Sumino, `Algorithms to evaluate multiple sums for loop computations,' J. Math. Phys. 54 (2013), art. 033514 (22pp); preprint 1211.5204[hep-th].
J. Ablinger and J. Blümlein, `Harmonic sums, polylogarithms, special numbers, and their generalizations,' in Computer Algebra in Quantum Field Theory, C. Schneider and J. Blümlein (eds.), Springer, Vienna, 2013, pp. 1-32; preprint 1304.7071[math-ph].
J. Furuya, M. Minamide, and Y. Tanigawa, `Moment integrals of 1/sin t and related zeta-values,' Ramanujan J. 33 (2014), 423-445.
I. Mező, `Nonlinear Euler sums,' Pacific J. Math. 272 (2014), 201-226.
S. Agarwala, `Dihedral symmetry of multiple polylogarithms,' Commun. Number Theory Phys. 7 (2014), 57-124; preprint 1112.1474[NT].
I. Todorov, `Polylogarithms and multizeta values in massless Feynman amplitudes,' in Lie Theory and its Applications in Physics (Varna, 2013), V. Dobrev (ed.), Springer Proc. in Math. and Stat. 111, Springer, New York, 2014, pp. 155-175.
S. Yamamoto, `A sum formula of multiple L-values,' Int. J. Number Theory 11 (2015), 127-137; preprint 1101.3948[NT].
M-A. Coppo and B. Candelpergher, `Inverse binomial series and values of Arakawa-Kaneko zeta functions,' J. Number Theory 150 (2015), 98-119.
G. H. E. Duchamp, V. Hoang Ngoc Minh, and Ngo Quoc Hoan, `Harmonic sums and polylogarithms at negative multi-indices,' ACM Commun. Computer Algebra 49 (2015), 70-73.
J. M. Borwein and A. Straub, `Relations for Nielsen polylogarithms,' J. Approx. Theory 193 (2015), 74-88; preprint.
C. Bogner and M. Lüders, `Multiple polylogarithms and linearly reducible Feynman graphs,' in Feynman Amplitudes, Periods and Motives (Madrid, 2012), L. Álvarez-Cónsul et. al. (eds.), Contemp. Math. 648, Amer. Math. Soc., Providence, RI, 2015, pp. 11-28.
C. Duhr, `Scattering amplitudes, Feynman integrals and multiple polylogarithms,' in Feynman Amplitudes, Periods and Motives (Madrid, 2012), L. Álvarez-Cónsul et. al. (eds.), Contemp. Math. 648, Amer. Math. Soc., Providence, RI, 2015, pp. 109-134.
I. Soudères, `Cycle complex over P¹ minus 3 points: toward multiple zeta value cycles,' J. Pure Appl. Algebra 220 (2016), 2590-2647; preprint 1210.4653[AG].
D. H. Bailey and J. M. Borwein, `Computation and structure of character polylogarithms with applications to character Mordell-Tornheim-Witten sums,' Math. Comp. 85 (2016), 295-324.
H. Frellesvig, D. Tommasini, and C. Wever, `On the reduction of generalized polylogarithms to Li_n and Li_2,2 and on the evaluation thereof,' J. High Energy Phys. (2016) 03#189(35 pp).
M. N. Lalín, `A new method for obtaining polylogarithmic Mahler measure formulas,' Res. Number Theory 2:17 (2016) (16 pp.)
E. Panzer, `The parity theorem for multiple polylogarithms,' J. Number Theory 172 (2017), 93-113; preprint 1512.04482[NT].
H. Furusho, Y. Komori, K. Matsumoto, and H. Tsumura, `Fundamentals of p-adic multiple L-functions and evaluation of their special values,' Selecta Math. (N. S.) 23 (2017), 39-100; preprint 1508.07185[NT].
J. M. Henn, A. V. Smirnov, and V. A. Smirnov, `Evaluating multiple polylogarithm values at sixth roots of unity up to weight six,' J. Nuclear Phys. B 919 (2017), 315-324; preprint 1512.08389[hep-th].
M. E. Hoffman and K. Ihara, `Quasi-shuffle products revisited,' J. Algebra 481 (2017), 293-326; preprint 1610.05180[QA].
G. H. E. Duchamp, V. Hoang Ngoc Minh, and Ngo Quoc Hoan, `Harmonic sums and polylogarithms at non-positive multi-indices,' J. Symbolic Comput. 83 (2017), 166-186; preprint 1611.09683[CO].
E. D'Hoker, M. B. Green, Ö. Güdoğan, and P. Vahnove, `Modular graph functions,' Commun. Number Theory Phys. 11 (2017), 165-218; preprint 1512.06779[hep-th].
K. Ebrahimi-Fard, D. Manchon, and J. Singer, `The Hopf algebra of (q)multiple polylogarithms with nonpositive arguments,' Int. Math. Res. Notices 2017, 4882-4922; preprint 1503.02977[NT].
S. Gun and B. Saha, `Multiple Lerch zeta functions and an Idea of Ramanujan,' Michigan Math. J. 67 (2018), 267-287.
O. Schnetz, `Numbers and functions in quantum field theory,' Phys. Rev. D 97 (2018), art. 085018 (20 pp).
D. H. Bailey and J. M. Borwein, `Computation and experimental evaluation of Mordell-Tornheim-Witten sum derivatives,' Experiment. Math. 27 (2018), 370-376.
M. N. Lalín and J-S. Lechausseur, `A reduction formula for length-two polylogarithms and some applications,' Rev. Un. Math. Argentina 59 (2018), 285-309.
O. Schnetz, `The Galois coaction on the electron anomalous magnetic moment,' Commun. Number Theory Phys. 12 (2018), 335-354; preprint 1711.05118[hep-th].
B. Saha, `Analytic properties of multiple Dirichlet series associated to additive and Dirichlet characters,' Manuscripta Math. 159 (2019), 203-227; cf. preprint 1705.05341[NT].
M. Ono, `New functional equations of finite multiple polylogarithms,' Tohoku Math. J. (2)72 (2020), 149-157; preprint 1706.09136[NT].
J. Écalle, `The scrambling operators applied to multizeta algebra and singular perturbation analysis,' in Algebraic Combinatorics, Resurgence, Moulds and Applications, vol. 2, F. Chapoton et. al (eds.), European Math. Soc. Publ. House, Berlin, 2020, pp. 133-325.
M. E. Hoffman, `Quasi-shuffle algebras and applications,' in Algebraic Combinatorics, Resurgence, Moulds and Applications, vol. 2, F. Chapoton et. al (eds.), European Math. Soc. Publ. House, Berlin, 2020, pp. 327-348; preprint 1805.12464[NT].
S. Yamamoto, `Multivariable Hoffman-Ihara operators and the operad of formal power series, J. Algebra 556 (2020), 634-648.
K. Ebrahimi-Fard, W. S. Gray, and D. Manchon, `Evaluating generating functions for periodic multiple polylogarithms via rational Chen-Fliess series,' in Periods in Quantum Field Theory and Arithmetic (ICMAT, Madrid, 2014), J. I. Burgos Gil et. al. (eds.), Springer Proc. in Math. & Stat. 314, Springer, New York, 2020, pp. 445-468; preprint 1603.05948[NT].
K. Tasaka, `Finite and symmetric colored multiple zeta values and multiple harmonic q-series at roots of unity,' Selecta Math. (N. S.) 27 (2021), art. 21 (34 pp.); preprint 1907.01935[NT].
M. Kato and Y. Takeyama, `A deformantion of multiple L-values,' Ramanujan J. 57 (2022), 93-118.
H. Kawamura, T. Maesaka, and S-I. Seki, Multivariable connected sums and multiple polylogarithms,' Res. Math. Sci. 9 (2022), art. 4 (25 pp.); preprint 2103.05492[NT].
H. Murahara and T. Onozuka, `Connectors of the Ohno relations for parametrized multiple series,' Rocky Mountain J. Math. 52 (2022), 687-694.
T. Tanaka, and N. Wakabayashi, `Rooted tree maps for multiple L-values, J. Number Theory 240 (2022), 471-489.
K.-G. Schlesinger, `Some remarks on q-deformed multiple polylogarithms,' preprint QA/0111022.
W. Zudilin, `One parameter models of Hopf algebras associated with multiple zeta values,' preprint.
S. Oi, `Representaion of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta values,' preprint NT/0405162.
N. Dan, `Sur la conjecture de Zagier pour n=4,' preprint 0809.3984[KT].
N. Dan, `Sur la conjecture de Zagier pour n=4 II,' preprint 1101.1557[KT].
S. Oi and K. Ueno, `Connection problem of Knizhnik-Zamolodchikov equation on moduli space M_0,5,' preprint 1109.0715[QA].
C. Duhr, `Mathematical aspects of scattering amplitudes,' preprint 1411.7538[hep-ph].
C. Glanois, `Unramified Euler sums and Hoffman ★ basis,' preprint 1603.05178[NT].
H. Gangl, `Multiple polylogarithms in weight 4,' preprint 1609.05557[NT].
S. Charlton, `A review of Dan's reduction method for multiple polylogarithms,' preprint 1703.03961[NT].
C. Xu, `Evaluations of multiple polylogarithm functions, multiple zeta values and related zeta values,' preprint 1908.03065[NT].
S. Kadota, `On the parity result for multiple Dirichlet series,' preprint 1909.06062[NT].
R. Umezawa, `Evaluation of iterated log-sine integrals in terms of multiple polylogarithms,' preprint 1912.07201[NT].
K. C. Au, `Evaluation of one-dimensional polylogarithmic integral, with applications to infinite series,' preprint 2007.03957[NT]
S. Yamamoto, `Duality of one-variable multiple polylogarithms and their q-analogues,' preprint 2010.05505[NT].
Z-h. Li and Z. Wang, `Weighted sum formulas of multiple L-values and its applications,' preprint 2102.07184[NT].
C. Xu and Z. Zhao, `Explicit relations of some variants of convoluted multiple zeta values,' preprint 2103.01377[NT].
K. C. Au, `Iterated integrals and special values of multiple polylogarithms at algebraic arguments,' preprint 2201.01676[NT].
M. Kaneko and H. Tsumura, `Multiple L-values of level four, poly-Euler numbers, and related zeta functions,' preprint 2208.05146[NT].

G. ELLIPTIC MULTIPLE ZETA VALUES

J. Brödel, C. R. Mafra, N. Matthes, and O. Schlotterer, `Elliptic multiple zeta values and one-loop superstring amplitudes,' J. High Energy Phys. (2015) 07#112 (41 pp).
J. Brödel, N. Matthes, and O. Schlotterer, `Relations between elliptic multiple zeta values and a special derivation algebra,' J. Phys. A: Math. Theor. 49 (2016), 155203 (49 pp.); preprint 1507.02254[hep-th].
B. Enriquez, `Analogues elliptiques des nombres multizétas,' Bull. Math. Soc. France 144 (2016), 395-427.
N. Matthes, `Elliptic double zeta values,' J. Number Theory 171 (2017), 227-251; preprint 1509.08760[NT].
S. Hohenegger and S. Stieberger, `Monodromy relations in higher-loop string amplitudes,' Nuclear Phys. B 925 (2017), 63-134; preprint 1702.04963[NT].
N. Matthes, `Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals,' in Various Aspects of Multiple Zeta Value, H. Furusho (ed.), RIMS Kōkyūroku 2015 (2017), pp. 170-183; preprint 1703.09597[NT].
J. Brödel, N. Matthes, G. Richter, and O. Schlotterer, `Twisted elliptic multiple zeta values and non-planar one-loop open string amplitudes,' J. Phys. A: Math. Theor. 51 (2018), 285401 (49 pp.); preprint 1704.03449[hep-th].
J. Brödel, O. Schlotterer, and F. Zerbini, From elliptic multiple zeta values to modular graph functions: open and closed strings at one loop,' J. High Energy Phys. (2019) 01#155 (67pp).
J. Brödel, C. Duhr, F. Dulat, B. Penante, and L. Tancredi, `From modular forms to differential equations for Feynman diagrams,' in Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, C. Schneider and P. Paule (eds.), Springer, New York, 2019, pp, 107-131; preprint 1807.00842[hep-th].
J. Brödel and O. Schlotterer, `One-loop string scattering amplitudes as iterated Eisenstein integrals,' in Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory, J. Blümlein, C. Schneider and P. Paule (eds.), Springer, New York, 2019, pp, 133-159.
L. Schneps, `Elliptic double shuffle, Grothendieck-Teichmüller and mould theory,' Ann. Math. Qué 44 (2020), 261-289; preprint 1506.09050[NT].
N. Matthes, `Overview on elliptic multiple zeta values,' in Periods in Quantum Field Theory and Arithmetic (ICMAT, Madrid, 2014), J. I. Burgos Gil et. al. (eds.), Springer Proc. in Math. & Stat. 314, Springer, New York, 2020, pp. 105-132.
P. Lochak, N. Matthes, and L. Schneps, `Elliptic multiple zeta values and the elliptic double shuffle relations,' Int. Math. Res. Notices 2021, 695-753; preprint 1703.09410[NT].

H. FINITE MULTIPLE HARMONIC SUMS

J. Blümlein and S. Kurth, `Harmonic sums and Mellin transforms up to two-loop order,' Phys. Rev. D 60 (1999), art. 01418 (31 pp); preprint hep-ph9810241.
J. A. M. Vermaseren, `Harmonic sums, Mellin transforms and integrals,' Int. J. Modern Phys. A 14 (1999), 2037-2076; preprint hep-ph9806280.
S. Moch and J. A. M. Vermaseren, `Deep inelastic structure functions at two loops,' Nuclear Phys. B 573 (2000), 853-907; preprint hep-ph9912355.
J. Blümlein, `Analytic continuation of Mellin transforms up to two-loop order,' Comput. Phys. Commun. 133 (2000), 76-104; preprint hep-ph0003100.
J. Blümlein, `Algebraic relations between harmonic sums and associated quantities,' Comput. Phys. Commun. 159 (2004), 19-54; preprint hep-ph0311046.
M. E. Hoffman, `The Hopf algebra structure of multiple harmonic sums,' Nuclear Phys. B (Proc. Suppl.) 135 (2004), 214-219; preprint QA/0406589.
A. I. Davydychev and M. Yu. Kalmykov, `Massive Feynman diagrams and inverse binomial sums,' Nuclear Phys. B 699 (2004), 3-64; preprint hep-th/0303162.
J. Blümlein and S. Moch, `Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions,' Phys. Lett. B 614 (2005), 53-61; preprint hep-ph/0503188.
C-G. Ji, `A simple proof of a curious congruence by Zhao,' Proc. Amer. Math. Soc. 133 (2005), 3469-3472.
D. M. Bradley, `Duality for finite multiple harmonic q-series', Disc. Math. 300 (2005), 44-56.
C. Costermans, J-Y. Enjalbert and V. Hoang Ngoc Minh, `Algorithmic and combinatoric aspects of multiple harmonic sums,' in 2005 International Conference on Analysis of Algorithms, C. Martínez (ed.), DMTCS Conference Vol. AD (2005), pp. 59-70.
C. Costermans, J-Y. Enjalbert, V. Hoang Ngoc Minh and M. Petitot, `Structure and asymptotic expansion of multiple harmonic sums,' in International Symposium on Symbolic and Algebraic Computation (Beijing, 2005), M. Kauers (ed.), ACM Press, New York, 2005, pp. 100-107.
C. Costermans and V. Hoang Ngoc Minh, `Some results à l'Abel obtained by use of techniques à la Hopf,' in Global Integrability of Field Theories (Daresbury, UK, 2006), J. Calmet et. al. (eds.), Universitätsverlag Karlsruhe, 2006, pp. 63-83.
C. Sekine, `Partial sums of multiple zeta value series,' Tokyo J. Math. 29 (2006), 465-474.
J. Zhao, `Bernoulli numbers, Wolstenholme's theorem, and p⁵ variations of Lucas' theorem,' J. Number Theory 123 (2007), 18-26.
X. Fu, X. Zhou, and T. Cai, `Congruences for finite triple harmonic sums,' J. Zhejiang Univ. Science A 8 (2007), 946-948.
X. Zhou and T. Cai, `A generalization of a curious congruence on harmonic sums,' Proc. Amer. Math. Soc. 135 (2007), 1329-1333.
J. Zhao, `Wolstenholme type theorem for multiple harmonic sums,' Int. J. Number Theory 4 (2008), 73-106; preprint NT/0301252.
M. Kuba, H. Prodinger, and C. Schneider, `Generalized reciprocity laws for sums of harmonic numbers,' Integers 8(1) (2008), #A17 (20 pp).
S. Albino, `Analytic continuation of harmonic sums,' Phys. Lett. B 674 (2009), 41-48.
C. Costermans and V. Hoang Ngoc Minh, Noncommutative algebra, multiple harmonic sums and applications in discrete probability, J. Symbolic Comput. 44 (2009), 801-817.
J. Blümlein, `Structural relations of harmonic sums and Mellin transforms up to weight w = 5,' Comput. Phys. Commun. 180 (2009), 2218-2249; preprint 0901.3106[hep-ph].
G. Kawashima, `A generalization of the duality for multiple harmonic sums,' J. Number Theory 130 (2010), 347-359; preprint 0802.1228[NT].
M. Kuba and H. Prodinger,`On a reciprocity law for finite multiple zeta values,' Int. J. Combinatorics 2010, art. 153621 (13 pp).
M. Kuba and H. Prodinger, `A note on Stirling series,' Integers 10 (2010), #A34, 393-406.
R. Tauraso, `Congruences involving alternating multiple harmonic sums,' Electronic J. Combinatorics 17(1) (2010), R16 (11 pp).
M. Kuba, `On functions of Arakawa and Kaneko and multiple zeta functions,' Appl. Anal. Discrete Math. 4 (2010), 45-53.
R. Tauraso, `New harmonic number identities with applications,' Sém. Lothar. Combin. 63 (2010), art. B63g (8 pp).
G. Kawashima, `A generalization of the duality for finite multiple harmonic q-series,' Ramanujan J. 21 (2010), 335-347; preprint 0905.0244[NT].
R. Tauraso and J. Zhao, `Congruences of alternating multiple harmonic sums,' J. Comb. Number Theory 2 (2010), 129-159; preprint 0909.0670[NT].
B. Xia and T. Cai, `Bernoulli numbers and congruences for harmonic sums,' Int. J. Number Theory 6 (2010), 849-855.
J. Blümlein, `Structural relations of harmonic sums and Mellin transforms at weight w = 6,' in Motives, Quantum Field Theory and Pseudodifferential Operators (Boston, 2008), A. Carey et. al. (eds.), Clay Math. Proc. 12, Amer. Math. Soc., Providence, RI, 2010, pp. 167-187; preprint 0901.0837[math-ph].
J. Ablinger, J. Blümlein and C. Schneider, `Harmonic sums and polylogarithms generated by cyclotomic polynomials,' J. Math. Phys. 52 (2011), art. 102301 (52 pp); preprint 1105.6063[math-ph].
J. Zhao, `Mod p structure of alternating and non-alternating multiple harmonic sums,' J. Théor. Nombres Bordeaux 23 (2011), 299-308.
Kh. Hessami Pilehrood and T. Hessami Pilehrood, `Congruences arising from Apéry-type series for zeta values,' Adv. Appl. Math. 49 (2012), 218-238; preprint 1108.1893[NT].
J. Zhao, `Finiteness of p-divisible sets of multiple harmonic sums,' Ann. Sci. Math. Québec 36 (2012), 419-443; preprint NT/0303043.
J. Zhao, `On q-analog of Wolstenholme type congruences for multiple harmonic sums,' Integers 13 (2013) , #A23 (11 pp).
Z. Shen and T. Cai, `Congruences for alternating triple harmonic series' (Chinese), Acta Math. Sinica (Chin. Ser.) 55 (2012), 737-748.
A. Ablinger, J. Blümlein, and C. Schneider, `Analytic and algebraic aspects of generalized harmonic sums and polylogarithms,' J. Math. Phys. 54 (2013), art. 082301 (73 pp); preprint 1302.0378[math-ph].
J. Rosen, `Multiple harmonic sums and Wolstenholme's theorem,' Int. J. Number Theory 9 (2013), 2033-2052; preprint 1302.0073[NT].
K. Imatomi, M. Kaneko, and E. Takeda, `Multi-poly-Bernoulli numbers and finite multiple zeta values,' J. Integer Sequences 17 (2014), art. 14.4.5 (12 pp).
Kh. Hessami Pilehrood, T. Hessami Pilehrood, and R. Tauraso, `New properties of multiple harmonic sums modulo p and p-analogues of Leshchiner's series,' Trans. Amer. Math. Soc. 366 (2014), 3131-3159; preprint 1206.0407[NT].
L. Wang and T. Cai, `A curious congruence modulo prime powers,' J. Number Theory 144 (2014), 15-24.
J. Ablinger, J. Blümlein, C. G. Raab, and C. Schneider, `Iterated binomial sums and their associated iterated integrals,' J. Math. Phys. 55 (2014), art. 112301 (57 pp); preprint 1407.1822[math-ph].
J. Ablinger, J. Blümlein, and C. Scheider, `Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers, J. Phys. Conf. Ser. 523 (2014), art. 012060 (10 pp); preprint 1310.5645[math-ph].
K. Imatomi, `Multi-poly-Bernoulli-star numbers and finite multiple zeta-star values,' Integers 14 (2014), #A51 (10 pp).
E. Linebarger and J. Zhao, `A family of multiple harmonic sum and multiple zeta star value identities,' Mathematika 61 (2015), 63-71; preprint 1304.3927[NT].
J. Rosen, `Asymptotic relations for truncated multiple zeta values,' J. London Math. Soc. (2) 91 (2015), 554-572; preprint 1309.0908[NT].
L. Wang, `A new curious congruence involving multiple harmonic sums,' J. Number Theory 154 (2015), 16-31.
S. Saito and N. Wakabayashi, `Sum formula for finite multiple zeta values,' J. Math. Soc. Japan 67 (2015), 1069-1076; preprint 1305.6529[NT].
M. E. Hoffman, `Quasi-symmetric functions and mod p multiple harmonic sums,' Kyushu J. Math. 69 (2015), 345-366.
K. Kamano, `Finite Mordell-Tornheim multiple zeta values,' Funct. Approx. Comment. Math. 54 (2015), 65-72.
S. Saito and N. Wakabayashi, `Bowman-Bradley type theorem for finite multiple zeta values,' Tohoku Math. J. (2) 68 (2016), 241-251; preprint 1304.2608[NT].
J. Zhao, `Identity families of multiple harmonic sums and multiple zeta (star) families,' J. Math. Soc. Japan 68 (2016), 1669-1694; preprint 1303.2227[NT].
K. Sakugawa and S-I. Seki, `On functional equations of finite multiple polylogarithms,' J. Algebra 469 (2017), 323-357; preprint 1509.07653[NT].
M. McCoy, K. Thielen, L. Wang, and J. Zhao, `A family of super congruences involving multiple harmonic sums,' Int. J. Number Theory 13 (2017), 109-128.
M. Ono and S. Yamamoto, `Shuffle product of finite multiple polylogarithms,' Manuscripta Math. 152 (2017), 153-166; preprint 1502.06693[NT].
K. Sakugawa and S-I. Seki, `Finite and étale polylogarithms,' J. Number Theory 176 (2017), 279-301; preprint 1603.05811[NT].
T. Cai, Z. Shen and L. Jia, `A congruence involving harmonic sums modulo p^αq^β,' Int. J. Number Theory 13 (2017), 1083-1094; preprint 1503.02798[NT].
K. Chen and J. Zhao, `Supercongruences involving multiple harmonic sums and Bernoulli numbers,' J. Integer Sequences 20 (2017), art. 17.6.8 (22 pp).
Kh. Hessami Pilehrood, T. Hessami Pilehrood, and T. Tauraso, `Multiple harmonic sums and multiple harmonic star sums are (nearly) never integers,' Integers 17 (2017), #A10 (12 pp).
P. Yang and T. Cai, `Super congruences on harmonic sums,' Int. J. Number Theory 13 (2017), 2569-2582.
J. Zhao, `Some congruences related to finite multiple zeta values,' Anal. Geom. Number Theory 2 (2017), 59-75; preprint 1404.3549[NT].
G. Yamashita, `A small remark on finite multiple zeta values and p-adic multiple zeta values,' in Various Aspects of Multiple Zeta Values (Kyoto, 2013), K. Ihara (ed.), RIMS Kōkyūroku Bessatsu B68, 2017, pp. 171-174.
S. Saito, `Numerical tables for finite multiple zeta values,' in Various Aspects of Multiple Zeta Values (Kyoto, 2013), K. Ihara (ed.), RIMS Kōkyūroku Bessatsu B68, 2017, pp. 191-208.
K. Kamano, `Weighted sum formulas for finite multiple zeta values,' J. Number Theory 192 (2018), 168-180.
K. Chen, R. Hong, J. Qu, David Wang, and J. Zhao, `Some families of super congruences involving multiple harmonic sums,' Acta Arithmetica 185 (2018), 201-210; preprint 1702.08599[NT].
K. Oyama, `Ohno-type relation for finite multiple zeta values,' Kyushu J. Math. 72 (2018), 277-285.
Y. Komori, `Finite multiple zeta values, multiple zeta functions and multiple Bernoulli polynomials,' Kyushu J. Math. 72 (2018), 333-342.
T. Cai and Z. Shen, `Congruences involving alternating harmonic sums modulo p^αq^β,' Math. Slovaca 68 (2018), 975-980; preprint 1503.03154[NT].
Y. Wang and J. Yang, `Modulo p² congruences involving harmonic numbers,' Ann. Polon. Math. 121 (2018), 263-278.
S-I. Seki, `The p-adic duality for the finite star-multiple polylogarithms,' Tohoku Math. J. (2) 71 (2019), 111-122; preprint 1605.06739[NT].
A. Prygarin, `Reflection identities of harmonic sums of weight four,' Universe 5(3) (2019), art. 77 (24 pp).
Z-h. Li and E. Pan, `Sum of interpolated finite multiple harmonic q-series,' J. Number Theory 201 (2019), 148-175; preprint 1811.09199[NT].
H. Hirose, M. Murahara, and S. Saito, `Weighted sum formulas for multiple harmonic sums modulo primes,' Proc. Amer. Math. Soc. 147 (2019), 3357-3366; preprint 1808.00844[NT].
M. Kaneko, K. Oyama, and S. Saito, `Analogues of the Aoki-Ohno and Le-Murakami relations for finite multiple zeta values,' Bull. Aust. Math. Soc. 100 (2019), 34-40; preprint 1810.04813[NT].
L. Jiu and D. Y. Shi, `Matrix representation for multiplicative nested sums,' Colloq. Math. 158 (2019), 183-194; preprint 1611.02425[CO].
J. Rosen, `The completed finite period map and Galois theory of supercongruences,' Int. Math. Res. Notices 2019, 7379-7405; preprint 1703.04248[NT].
M. Joubat and A. Prygarin, `The analytic structure of the BFKL equation and reflection identities of harmonic sums at weight five,' Internat. J. Modern Phys. A 34 (2019), art. no. 1950064 (122 pp).
S-I. Seki and S. Yamamoto, `Ohno-type identities for multiple harmonic sums,' J. Math. Soc. Japan 72 (2020), 673-686; preprint 1806.04785[NT].
H. Murahara, T. Onozuka, and S-I. Seki, `Bowman-Bradley type theorem for finite multiple zeta values in 𝒜₂,' Osaka J. Math. 57 (2020), 647-653; preprint 1810.10803[NT].
H. Bachmann, Y. Takeyama, K. Tasaka, `Special values of finite multiple harmonic q-series at roots of unity,' in Algebraic Combinatorics, Resurgence, Moulds and Applications, vol. 2, F. Chapoton et. al (eds.), European Math. Soc. Publ. House, Berlin, 2020, pp. 1-18; preprint 1807.00411[NT].
N. Kawasaki and K. Oyama, `Cyclic sums of finite multiple zeta values,' Acta Arithmetica 195 (2020), 281-288.
H. Murahara and T. Onozuka, `Derivation relation for finite multiple zeta values in 𝒜̂,' J. Aust. Math. Soc. 110 (2021), 260-265; preprint 1809.02752[NT].
L. Wang, `New congruences on multiple harmonic sums and Bernoulli numbers', Publ. Math. Debrecen 97 (2020), 161-180; preprint 1504.03227[NT].
Y. Wang and J. Yang, `Modulo p² congruences involving generalized harmonic numbers,' Bull. Malays. Math. Soc. Sci. 44 (2021), 1799-1812.
H. Murahara and M. Ono, `Yamamoto's interpolation of finite multiple zeta and zeta-star values,' Tokyo J. Math. 44 (2021), 285-312; preprint 1908.09307[NT].
M. Kuba, `On multisets, interpolated multiple zeta values and limit laws,' Electron. J. Combin. 29(1) art. p1.48 (30 pp.).
G. Kawashima, `Multiple series expressions for the Newton series which interpolate finite multiple harmonic sums,' preprint 0905.0243[NT].
T. Cai and Z. Shen, `Super congruences involving alternating harmonic sums modulo prime powers,' preprint 1503.03156[NT].
J. Zhao, `Finite multiple zeta values and finite Euler sums,' preprint 1507.04917[NT].
J. Rosen, `The MHS algebra and supercongruences,' preprint 1608.06864[NT].
A. Prygarin, `Reflection identities of harmonic sums up to weight three,' preprint 1808.09307[hep-th].
Y. Takeyama and K. Tasaka, `Supercongruences of multiple harmonic q-sums and generalized finite/symmetric multiple zeta values,' preprint 2012.07067[NT].
Kh. Hessami Pilehrood, T. Hessami Pilehrood, and R. Tauraso, `On 3-2-1 values of finite multiple harmonic q-series at roots of unity,' preprint 2101.03576[NT].
D. Matsuzuki,`Alternating variants of of multiple poly-Bernoulli numbers and finite multiple zeta values in characteristic 0 and p,' preprint 2103.13118[NT].
M. Kaneko, T. Murakami, and A. Yoshihara, `On finite multiple zeta values of level two,' preprint 2109.12501[NT].
S. Chen, `On a congruence involving harmonic series and Bernoulli numbers,' preprint 2110.09629[NT].
T. Anzawa, `Weighted sum formulas for finite alternating multiple zeta values with some parameters,' preprint 2201.02027[NT].
Z-h. Li and Z. Wang, `Integrality and some evaluations of odd multiple harmonic sums,' preprint 2204.01347[NT].

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