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

  1. P. H. Fuss (ed.), Correspondance Mathématique et Physique de quelques célèbres Géomètres (Tome 1), St. Petersburg, 1843.
  2. 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.
  3. N. Nielsen, Die Gammafunktion, Chelsea, New York, 1965. Reprint of Handbuch der Theorie der Gammafunktion (1906) and Theorie der Integrallogarithmus und verwandter Transzendenten (1906).
  4. F. V. Atkinson, `The mean value of the Riemann zeta function,' Acta Math. 81 (1949), 353-376.
  5. L. Tornheim, `Harmonic double series,' Amer. J. Math. 72 (1950), 303-314.
  6. G. T. Williams, `A new method of evaluating ζ(2n),' Amer. Math. Monthly 60 (1953), 19-25.
  7. P. F. Jordan, `Infinite sums of psi functions,' Bull. Amer. Math. Soc. 79 (1973), 681-683.
  8. T. M. Apostol and T. H. Vu, `Dirichlet series related to the Riemann zeta function,' J. Number Theory 19 (1984), 85-102.
  9. M. V. Subbarao and R. Sitaramachandrarao, `On some infinite series of L. J. Mordell and their analogues', Pacific J. Math. 119 (1985), 245-255.
  10. R. E. Crandall and J. P. Buhler, `On the evaluation of Euler sums,' Experiment. Math. 3 (1994), 275-285.
  11. 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.
  12. L-C. Shen, `Remarks on some integrals and series involving the Stirling numbers and ζ(n)', Trans. Amer. Math. Soc. 347 (1995), 1391-1399.
  13. J. G. Huard, K. S. Williams, and N-Y. Zhang, `On Tornheim's double series,' Acta Arithmetica 75 (1996), 105-117.
  14. M-A. Coppo, `Sur les sommes d'Euler divergentes,' Expositiones Mathematicae 18 (2000), 297-308.
  15. Wenchang Chu, `Symmetric functions and the Riemann zeta series,' Indian J. Pure Appl. Math. 31 (2000), 1677-1689.
  16. A. Basu and T. M. Apostol, `A new method of investigating Euler sums,' Ramanujan J. 4 (2000), 397-419.
  17. K. N. Boyadzhiev, `Evaluation of Euler-Zagier sums,' Internat. J. Math. Math. Sci. 27 (2001), 407-412.
  18. K. N. Boyadzhiev, `Consecutive evaluation of Euler sums,' Internat. J. Math. Math. Sci. 29 (2002), 555-561.
  19. H. Tsumura, `On some combinatorial relations for Tornheim's double series,' Acta Arithmetica 105 (2002), 239-252.
  20. 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.
  21. 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.
  22. H. Tsumura, `On alternating analogues of Tornheim's double series,' Proc. Amer. Math. Soc. 131 (2003), 3633-3641.
  23. H. Tsumura, `Evaluation formulas for Tornheim's type of alternating double series,' Math. Comp. 73 (2004), 251-258.
  24. M. Jung, Y. J. Cho and J. Choi, `Euler sums evaluatable from integrals,' Commun. Korean Math. Soc. 19 (2004), 545-555.
  25. H. Tsumura, `On evaluation formulas for double L-values,' Bull. Austral. Math. Soc. 70 (2004), 213-221.
  26. D. Terhune, `Evaluation of double L-values,' J. Number Theory 105 (2004), 275-301.
  27. R. Masri, `The Herglotz-Zagier function, double zeta values, and values of L-series,' J. Number Theory 106 (2004), 219-237.
  28. K. Matsumoto, `Functional equations for double zeta-functions,' Math. Proc. Camb. Phil. Soc. 136 (2004), 1-7.
  29. 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.
  30. 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.
  31. H. Tsumura, `Certain functional relations for the double harmonic series related to the double Euler numbers,' J. Aust. Math. Soc. 79 (2005), 319-333.
  32. S. Kanemitsu, Y. Tanigawa, and M. Yoshimoto, `Convolution of multiple zeta values,' J. Math. Soc. Japan 57 (2005), 1167-1177.
  33. O. Espinosa and V. H. Moll, `The evaluation of Tornheim double sums, Part I,' J. Number Theory 116 (2006), 200-229; preprint CA/0505647.
  34. K-W. Chen and M. Eie, `Explicit evaluations of extended Euler sums,' J. Number Theory 117 (2006), 31-52.
  35. D. Terhune, `Evaluations of a class of double L-values,' Proc. Amer. Math. Soc. 134 (2006), 1881-1889.
  36. H. Tsumura, `On some functional relations between Mordell-Tornheim double L-functions and Dirichlet L-functions,' J. Number Theory 120 (2006), 161-178.
  37. 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.
  38. T. Nakamura, `A functional relation for the Tornheim zeta function,' Acta Arithmetica 125 (2006), 257-263.
  39. I. Kiuchi and Y. Tanigawa, `Bounds for double zeta-functions,' Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) 5 (2006), 445-464.
  40. H. Tsumura, `On certain polylogarithmic double series,' Arch. Math. (Basel) 88 (2007), 42-51
  41. H. Tsumura, `On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function,' Math. Proc. Camb. Phil. Soc. 142 (2007), 395-405.
  42. J. M. Borwein, `Hilbert's inequality and Witten's zeta-function,' Amer. Math. Monthly 115 (2008), 125-137.
  43. 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).
  44. X. Zhou, T. Cai, and D. M. Bradley, `Signed q-analogs of Tornheim's double series,' Proc. Amer. Math. Soc. 136 (2008), 2689-2698.
  45. M. Kuba, `On evaluations of infinite double sums and Tornheim's double series,' Sém. Lothar. Combin. 58 (2008), art. B58d (13 pp).
  46. J. M. Borwein, I. J. Zucker, and J. Boersma, `The evaluation of character Euler double sums,' Ramanujan J. 15 (2008), 377-405.
  47. A. Basu, `A new method in the study of Euler sums,' Ramanujan J. 16 (2008), 7-24.
  48. 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.
  49. 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.
  50. K. Matsumoto and H. Tsumura, `Functional relations among certain double polylogarithms and their character analogues,' Šialiai Math. Semin. 3(11) (2008), 189-205.
  51. T. Nakamura, `Double Lerch series and their functional relations,' Aequationes Math. 75 (2008), 251-259.
  52. H. Tsumura, `On alternating analogues of Tornheim's double series II', Ramanujan J. 18 (2009), 81-90.
  53. T. Nakamura, `Restricted and weighted sum formulas for double zeta values of even weight,' Šialiai Math. Semin. 4(12) (2009), 151-155.
  54. M. Eie and W-C. Liaw, `Double Euler sums on Hurwitz zeta functions,' Rocky Mountain J. Math. 39 (2009), 1869-1883.
  55. 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].
  56. 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.
  57. O. Espinosa and V. H. Moll, `The evaluation of Tornheim double sums, Part II,' Ramanujan J. 22 (2010), 55-99; preprint 0811.0557[NT].
  58. J. Zhao, `A note on colored Tornheim's double series,' Integers 10 (2010), #A59, 879-882.
  59. I. Kiuchi, Y. Tanigawa, and W. Zhai, `Analytic properties of double zeta-functions,' Indag. Math. 21 (2011), 16-29.
  60. A. Basu, `On the evaluation of Tornheim sums and allied double sums,' Ramanujan J. 26 (2011), 193-207.
  61. T. Okamoto, `Some relations among Apostol-Vu double zeta functions for coordinatewise limits at non-positive integers,' Tokyo J. Math. 34 (2011), 353-366.
  62. Y. Komori, K. Matsumoto, and H. Tsumura, `Functional equations for double L-functions at values at non-positive integers, Int. J. Number Theory 7 (2011), 1441-1461.
  63. 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.
  64. T. Nakamura, `A simple proof of the functional equation for the Lerch type Tornheim double zeta function,' Tokyo J. Math. 35 (2012), 333-337; preprint 1012.1144[NT].
  65. T. Nakamura and K. Tasaka, `Remarks on double zeta values of level 2,' J. Number Theory 133 (2013), 48-54.
  66. 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].
  67. T. Machide, `Some restricted sum formulas for double zeta values,' Proc. Japan Acad. Ser. A 89 (2013), 51-54; preprint 1210.7997[NT].
  68. 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 Statistics 43, Springer, New York, 2013, pp. 361-379; preprint 1206.2424[NT].
  69. S. Baumard and L. Schneps, `Period polynomial relations between double zeta values,' Ramanujan J. 32 (2013), 83-100; preprint 1109.3786[NT].
  70. 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].
  71. 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 Mathematics and Statistics 50, Springer, New York, 2013, pp. 113-126.
  72. 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.
  73. K. Dilcher, Kh. Hessami Pilehrood, and T. Hessami Pilehrood, On q-analogues of double Euler sums,' J. Math. Anal. Appl. 410 (2014), 979-988.
  74. D. M. Bradley, `A signed analog of Euler's reduction formula for the double zeta function,' preprint 0707.4486[CA].
  75. Z-h. Li,`On functional relations for the alternating analogues of Tornheim's double zeta function,' preprint 1011.2897[NT].
  76. K. Matsumoto and H. Tsumura, `Mean value theorems for the double zeta-function,' preprint 1203.2242[NT].
  77. K. Onodera, `A functional relation for Tornheim's double zeta functions,' preprint 1211.1480[NT].
  78. 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].
  79. S. Ikeda, K. Matsuoka, and Y. Nagata, `On certain mean values of the double zeta-function,' preprint 1303.6505[NT].
  80. Y. Choie and K. Matsumoto, `Functional equations for double series of Euler type with coefficients,' preprint 1306.0987[NT].
  81. H. Yuan and J. Zhao, `Double shuffle relations of double zeta values and double Eisenstein series of level N,' preprint 1401.6699[NT].

B. TRIPLE HARMONIC SERIES

  1. R. Sitaramachandrarao and M. V. Subbarao, `Transformation formulae for multiple series,' Pacific J. Math. 113 (1984), 471-479.
  2. C. Markett, `Triple sums and the Riemann zeta function,' J. Number Theory 48 (1994), 113-132.
  3. 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).
  4. M. E. Hoffman and C. Moen, `Sums of triple harmonic series,' J. Number Theory 60 (1996), 329-331.
  5. 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).
  6. 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.
  7. 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.
  8. Y. L. Ong, M. Eie, and W-C. Liaw, `Explicit evaluation of triple Euler sums,' Int. J. Number Theory 4 (2008), 437-451.
  9. I. Kiuchi and Y. Tanigawa, `Bounds for triple zeta functions,' Indag. Math. (N. S.) 19 (2008), 97-114.
  10. T. Okamoto, `On alternating analogues of the Mordell-Tornheim triple zeta values,' J. Ramanujan Math. Soc. 28 (2013), 247-269.
  11. T. Machide, `Extended double shuffle relations and the generating functions of triple zeta values of any fixed weight,' Kyushu Math. J. 67 (2013), 281-307; preprint 1204.4085[NT].

C. MULTIPLE HARMONIC SERIES/MULTIPLE ZETA VALUES

  1. M. E. Hoffman, `Multiple harmonic series,' Pacific J. Math. 152 (1992), 275-290.
  2. 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.
  3. 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.
  4. T. Q. T. Le and J. Murakami, `Kontsevich's integral for the Kauffman polynomial,' Nagoya Math. J. 142 (1996), 39-65.
  5. A. Granville, `A decomposition of Riemann's zeta-function,' in Analytic Number Theory, Y. Motohashi (ed.), London Mathematical Society Lecture Note Series 247, Cambridge University Press, 1997, pp. 95-101.
  6. 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.
  7. M. E. Hoffman, `The algebra of multiple harmonic series,' J. Algebra 194 (1997), 477-495.
  8. R. E. Crandall, `Fast evaluation of multiple zeta sums,' Math. Comp. 67 (1998), 1163-1172.
  9. 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).
  10. 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.
  11. Y. Ohno, `A generalization of the duality and sum formulas on the multiple zeta values,' J. Number Theory 74 (1999), 39-43.
  12. T. Arakawa and M. Kaneko, `Multiple zeta values, poly-Bernoulli numbers, and related zeta functions,' Nagoya Math. J. 153 (1999), 189-209.
  13. T. Takamuki, `The Kontsevich invariant and relations of multiple zeta values,' Kobe J. Math. 16 (1999), 27-43.
  14. 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).
  15. J. Zhao, `Analytic continuation of multiple zeta functions,' Proc. Amer. Math. Soc. 128 (2000), 1275-1283.
  16. Hoang Ngoc Minh and M. Petitot, `Lyndon words, polylogarithms, and the Riemann ζ function,' Discrete Math. 217 (2000), 273-292.
  17. M. Waldschmidt, `Valeurs zêta multiples. Une introduction,' J. Théor. Nombres Bordeaux 12 (2000), 581-595.
  18. M. Kontsevich and D. Zagier, `Periods,' in Mathematics Unlimited--2001 and Beyond,, B. Engquist and W. Schmid (eds.), Springer, Berlin, 2001, pp. 771-808.
  19. 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.
  20. K. Ihara and T. Takamuki, `The quantum g2 invariant and relations of multiple zeta values,' J. Knot Theory Ramifications 10 (2001), 983-997.
  21. S. Akiyama and Y. Tanigawa, `Multiple zeta values at non-positive integers,' Ramanujan J. 5 (2001), 327-351.
  22. Y. Ohno and D. Zagier, `Multiple zeta values of fixed weight, depth, and height,' Indag. Math. (N. S.) 12 (2001), 483-487.
  23. 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.
  24. M. E. Hoffman, `Periods of mirrors and multiple zeta values,' Proc. Amer. Math. Soc. 130 (2002), 971-974.
  25. T. Terasoma, `Selberg integrals and multiple zeta values,' Compositio Math. 133 (2002), 1-24.
  26. P. Cartier, `Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents,' Astérisque 282 (2002), 137-173 (Sém. Bourbaki no. 885).
  27. U. Müller and C. Schubert, `A quantum field theoretical representation of Euler-Zagier sums,' Internat. J. Math. Math. Sci. 31 (2002), 127-148.
  28. T. Terasoma, `Mixed Tate motives and multiple zeta values,' Invent. Math. 149 (2002), 339-369; preprint AG/0104231.
  29. S. Fischler, `Formes linéaires en polyzêtas et intégrales multiples,' C. R. Acad. Sci. Paris, Ser. I 335 (2002), 1-4.
  30. 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.
  31. 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.
  32. K. Matsumoto, `The analytic continuation and the asymptotic behavior of certain multiple zeta-functions I', J. Number Theory 101 (2003), 223-243.
  33. D. Bowman, D. M. Bradley, and J. H. Ryoo, `Some multi-set inclusions associated with shuffle convolutions and multiple zeta values,' European J. Combin. 24 (2003), 121-127.
  34. M. E. Hoffman and Y. Ohno, `Relations of multiple zeta values and their algebraic expression,' J. Algebra 262 (2003), 332-347; preprint QA/0010140.
  35. W. Zudilin, `Algebraic relations for multiple zeta values' (Russian), Uspekhi Mat. Nauk 58 (2003), 3-32; English translation in Russian Math. Surveys 58 (2003), 1-29; preprint.
  36. H. Ishikawa and K. Matsumoto, `On the estimation of the order of Euler-Zagier multiple zeta-functions,' Illinois J. Math. 47 (2003), 1151-1166.
  37. M. Espie, J-C. Novelli, and G. Racinet, `Formal computations about multiple zeta values,' in From Combinatorics to Dynamical Systems (Strasbourg, 2002), F. Fauvet and C. Mitschi (eds.), IRMA Lect. Math. Theor. Phys. 3, de Gruyter, Berlin, 2003, pp. 1-16.
  38. D. Bowman and D. M. Bradley, `Resolution of some open problems concerning multiple zeta evaluations of arbitrary depth,' Compositio Math. 139 (2003), 85-100.
  39. J. Écalle, `ARI/GARI, la dimorphie et l'arithmétique des multizêtas: un premier bilan,' J. Théor. Nombres Bordeux 15 (2003), 411-478.
  40. H. Furusho, `The multiple zeta value algebra and the stable derivation algebra,' Publ. Res. Inst. Math. Sci. 39 (2003), 695-720; preprint NT/0011261.
  41. K. Matsumoto, `On Mordell-Tornheim and other multiple zeta-functions,' in Proceedings of the Session in Analytic Number Theory and Diophantine Equations, D. R. Heath-Brown and B. Z. Moroz (eds.), Bonner Math. Schriften 360, Univ. Bonn, Bonn, 2003, n. 25 (17 pp.).
  42. H. Żołądek, `Note on multiple zeta-values,' Bul. Acad. Ştiinţe Repub. Mold. Mat. 2003, 78-82.
  43. H. Furusho, `p-Adic multiple zeta values I. p-Adic multiple polylogarithms and the p-adic KZ equation,' Invent. Math. 155 (2004), 253-286; preprint NT/0304085.
  44. H. Tsumura, `Combinatorial relations for Euler-Zagier sums,' Acta Arithmetica 111 (2004), 27-42.
  45. H. Tsumura, `Multiple harmonic series related to multiple Euler numbers,' J. Number Theory 106 (2004), 155-168.
  46. J. Okuda and K. Ueno, `Relations for multiple zeta values and Mellin transforms of multiple polylogarithms,' Publ. Res. Inst. Math. Sci. 40 (2004), 537-564; preprint NT/0301277.
  47. S. Ünver, `p-Adic multi-zeta values,' J. Number Theory 108 (2004), 111-156.
  48. J. Écalle, `Recent advances in the analysis of divergence and singularities,' in Normal Forms, Bifurcations and Finiteness Problems in Differential Equations (Montreal, 2002), Y. Ilyashenko et. al. (eds.), Kluwer, Dordrecht, 2004, pp. 87-186.
  49. J. Écalle, `Multizetas, perinomal numbers, arithmetical dimorphy, and ARI/GARI,' Ann. Fac. Sci. Toulouse 13 (2004), 683-708.
  50. A. B. Goncharov and Yu. I. Manin, `Multiple ζ-motives and moduli spaces M0,n,' Compositio Math. 140 (2004), 1-14; preprint AG/0204102.
  51. A. J. Yee, `A new shuffle convolution for multiple zeta values,' J. Algebraic Combin. 21 (2005), 55-69.
  52. D. M. Bradley, `Multiple q-zeta values,' J. Algebra 283 (2005), 752-798; preprint QA/0402093.
  53. H. Tsumura, `On Mordell-Tornheim zeta values,' Proc. Amer. Math. Soc. 133 (2005), 2387-2393.
  54. T. Nakamura, `Bernoulli numbers and multiple zeta values,' Proc. Japan Acad. Ser. A Math. Sci. 81 (2005), 21-22.
  55. D. M. Bradley, `Partition identities for the multiple zeta function,' in Zeta Functions, Topology and Quantum Physics, T. Aoki et. al. (eds.), Developments in Math. 14, Springer, New York, 2005, pp. 19-29; preprint CO/0402091.
  56. M. E. Hoffman, `Algebraic aspects of multiple zeta values,' in Zeta Functions, Topology and Quantum Physics, T. Aoki et. al. (eds.), Developments in Math. 14, Springer, New York, 2005, pp. 51-74; preprint QA/0309425.
  57. Y. Ohno, `Sum relations for multiple zeta values,' in Zeta Functions, Topology and Quantum Physics, T. Aoki et. al. (eds.), Developments in Math. 14, Springer, New York, 2005, pp. 131-144.
  58. J. Okuda and K. Ueno, `The sum formula for multiple zeta values and connection problem of the formal Knizhnik-Zamolodchikov equation,' in Zeta Functions, Topology and Quantum Physics, T. Aoki et. al. (eds.), Developments in Math. 14, Springer, New York, 2005, pp. 145-170; preprint NT/0310259.
  59. M. Waldschmidt, `Hopf algberas and transcendental numbers,' in Zeta Functions, Topology and Quantum Physics, T. Aoki et. al. (eds.), Developments in Math. 14, Springer, New York, 2005, pp. 197-220.
  60. T. Aoki and Y. Ohno, `Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions,' Publ. Res. Inst. Math. Sci. 41 (2005), 329-337; preprint NT/0307264.
  61. J. Choi and H. M. Srivastava, `Explicit evaluation of Euler and related sums,' Ramanujan Journal 10 (2005), 51-70.
  62. P. Freitas, `Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums,' Math. Comp. 74 (2005), 1425-1440.
  63. J-W. Son and D. S. Jang, `Explicit evaluations of special multiple zeta values ζ({4l+2}n) and ζ({4l}n),' Commun. Korean Math. Soc. 20 (2005), 247-257.
  64. R. Masri, `Multiple Dedekind zeta functions and evaluations of extended multiple zeta values,' J. Number Theory 115 (2005), 295-309.
  65. M. Kaneko, `Multiple zeta values,' Sugaku Expositions 18 (2005), 221-232. (Translation of Japanese original that appeared in Sūgaku 54 (2002), 404-415.)
  66. E. A. Ulanskii, `Stuffle relations for multiple zeta values' (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2005, 52-55,73; English translation in Moscow Univ. Math. Bull. 60 (2005), 41-43.
  67. K. Matsumoto, `The analytic continuation and the asymptotic behavior of certain multiple zeta-functions III,' Comment. Math. Univ. St. Pauli 54 (2005), 163-186.
  68. S. A. Zlobin, `Generating functions for a multiple zeta function' (Russian), Vestnik Moskov. Univ. Ser. I Mat. Mekh. 2005, 55-59; English translation in Moscow Univ. Math. Bull. 60 (2005), 44-48.
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  220. L. Schneps, `Dual-depth adapted irreducible formal multizeta values,' Math. Scand. 113 (2013), 53-62.
  221. L. Guo, S. Paycha, and B. Zhang, `Conical zeta values and their double subdivision relations,' Adv. Math. 252 (2014), 343-381; preprint 1301.3370[NT].
  222. J. Zhao, `Sum formula of multiple Hurwitz-zeta values,' Forum Math. (to appear); preprint 1207.2368[NT].
  223. J. Okuda and K. Ueno, `New approach to Ohno relations for multiple zeta values,' preprint NT/0106148.
  224. S. Kitani, E. Sawada, and K. Ueno, `Finite automata and relations of multiple zeta values,' preprint NT/0403458.
  225. S. A. Zlobin, `A certain integral over a triangle,' preprint NT/0511239.
  226. S. A. Zlobin, `A note on arithmetic properties of multiple zeta values,' preprint NT/0501151.
  227. I. Horozov, `Multiple zeta values, modular forms, and adeles,' preprint NT/0611849.
  228. O. Mathieu, `On a symmetric space attached to polyzeta values,' preprint 0810.0396[NT].
  229. K. Imatomi, T. Tanaka, K. Tasaka, and N. Wakabayashi, `On some combinations of multiple zeta-star values,' preprint 0912.1951[NT].
  230. Y. Komori, K. Matsumoto and H. Tsumura, `Zeta-functions of weight lattices of compact connected semisimple Lie groups,' preprint 1011.00323[NT].
  231. I. Horozov, `Multiple Dedekind zeta values,' preprint 1101.1594[NT].
  232. J. Kuipers and J. A. M. Vermaseren, `About a conjectured basis for multiple zeta values,' preprint 1105.1884[math-ph].
  233. M. Igarashi, `Note on relations among multiple zeta-star values,' preprint 1106.0481[NT].
  234. M. Igarsahi, `On generalizations of the sum formula for multiple zeta values,' preprint 1110.4875[NT].
  235. Y. Komori, K. Matsumoto and H. Tsumura, `Functional relations for zeta-functions of weight lattices of type A3,' preprint 1202.0874[NT].
  236. Z-h. Li, `Another proof of Zagier's evaluation formula of the multiple zeta values ζ(2,...,2,3,2,...,2)' preprint 1204.2060[NT].
  237. Y. Komori, K. Matsumoto and H. Tsumura, `A study on multiple zeta values from the viewpoint of zeta-functions of root systems,' preprint 1205.0182[NT].
  238. O. Schlotterer and S. Stieberger, `Motivic multiple zeta values and superstring amplitudes,' preprint 1205.1516[hep-th].
  239. M. E. Hoffman, `On multiple zeta values of even arguments,' preprint 1205.7051[NT].
  240. G. Combariza, `A few conjectures about the multiple zeta values,' preprint 1207.1735[NT].
  241. J. Merker, `Multizeta calculus I,' preprint 1208.5643[NT].
  242. T. Machide, `A parametrized generalization of the sum formula for quadruple zeta values,' preprint 1210.8005[NT].
  243. J. M. Drummond and E. Ragoucy, `Superstring amplitudes and the associator,' preprint 1301.0794[hep-th].
  244. F. C. S. Brown, `Depth-graded motivic multiple zeta values,' preprint 1301.3053[NT].
  245. V. Baldoni, A. Boysal, and M. Vergne, `Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces,' preprint 1301.4127[RT].
  246. T. Terasoma, `Brown-Zagier relation for associators,' preprint 1301.7474[NT].
  247. Y. Komori, K. Matsumoto, and H. Tsumura, `On Witten multiple zeta-functions associated with semisimple Lie algebras V,' preprint 1302.4285[NT].
  248. S. Ünver, `Cyclotomic p-adic multi-zeta values in depth two,' preprint 1302.6406[NT].
  249. T. Tanaka, `Restricted sum formula and derivation relation for multiple zeta values,' preprint 1303.0398[NT].
  250. H. Yuan and J. Zhao, `Restricted sum formula of multiple zeta values,' preprint 1303.3607[NT].
  251. H. Yuan and J. Zhao, `New families of weighted sum formulas for multiple zeta values,' preprint 1303.3608[NT].
  252. Kh. Hessami Pilehrood and T. Hessami Pilehrood, `On q-analogues of two-one formulas for multiple harmonic sums and multiple zeta star values,' preprint 1304.0269[NT].
  253. J. Brödel, O. Schlotterer, S. Stieberger, and T. Terasoma, `All order alpha'-expansion of superstring trees from the Drinfeld associator,' preprint 1304.7304[hep-th].
  254. J-C. Novelli and J-Y. Thibon, `Binary shuffle bases for quasi-symmetric functions,' preprint 1305.5032[CO].
  255. S. Charlton, `ζ({{2}m,1, {2}m,3}n,{2}m)/π4n+2m(2n+1) is rational', preprint 1306.6775[NT].
  256. L. Guo, S. Paycha, and B. Zhang, `Renormalization of conical zeta values and the Euler-Maclaurin formula,' preprint 1306.3420[math-ph].
  257. Kh. Hessami Pilehrood, T. Hessami Pilehrood, and J. Zhao,`On q-analogs of some some families of multiple harmonic sum and multiple zeta star identities,' preprint 1307.7985[NT].
  258. S. Fischler and T. Rivoal, `Multiple zeta values, Padé approximation and Vasilyev's conjecture,' preprint 1309.2534[NT].
  259. J. Castillo Medina, K. Ebrahimi-Fard, and D. Manchon, `On Euler's decomposition formula for qMZVs,' preprint 1309.2759[NT].
  260. H. Bachmann and U. Kühn, `The algebra of multiple divisor functions and applications to multiple zeta values,' preprint 1309.3920[NT].
  261. F. C. S. Brown, `Single-valued periods and multiple zeta values,' preprint 1309.5309[NT].
  262. J. Castillo Medina, K. Ebrahimi-Fard, and D. Manchon, `Unfolding the double shuffle structure of qMZVs,' preprint 1310.1330[NT].
  263. S. Stieberger, `Closed superstring amplitudes, single-valued multiple zeta values and Deligne associator,' preprint 1310.3259[hep-th].
  264. I. Horozov, `Double shuffle relations for multiple Dedekind zeta values,' preprint 1311.4019[NT].
  265. L. Guo, P. Lei, and J. Zhao, `Familes of weighted sum formulas for multiple zeta values,' preprint 1401.6461[NT].
  266. L. Guo, P. Lei, and B. Ma,`Applications of shuffle product to restricted decomposition formulas for multiple zeta values,' preprint 1401.7397[NT].
  267. K. Tasaka, `On linear relations among totally odd multiple zeta values related to period polynomials,' preprint 1402.3391[NT].
  268. I. Todorov, `Polylogarithms and multizeta values in massless Feynman amplitudes,' IHES preprint P-14-10.

D. MULTIPLE ZETA VALUES OVER FUNCTION FIELDS

  1. D. Thakur, Function Field Arithmetic, World Scientific, Singapore, 2004.
  2. 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.
  3. G. W. Anderson and D. Thakur, `Multizeta values for Fq[t], their period interpretation, and relations between them,' Int. Math. Res. Notices 2009, 2038-2055; preprint 0902.1180[NT].
  4. D. Thakur, `Relations between multizeta values for Fq[t]', Int. Math. Res. Notices 2009, 2318-2346.
  5. D. Thakur, `Power sums with applications to multizeta and zeta zero distribution for Fq[t]', Finite Fields Appl. 15 (2009), 534-552.
  6. J. A. Lara Rodríguez, `Some conjectures and results about multizeta values over Fq[t]', J. Number Theory 130 (2010), 1013-1023.
  7. D. Thakur, `Shuffle relations for function field multiple zeta values,' Int. Math. Res. Notices 2010, 1973-1980.
  8. J. A. Lara Rodríguez, `Relations between multizeta values in characteristic p,' J. Number Theory 131 (2011), 2081-2099.
  9. J. A. Lara Rodríguez, `Special relations between multizeta values and parity results,' J. Ramanujan Math. Soc. 27 (2012), 275-293; preprint 1108.4726[NT].
  10. Chieh-Yu Chang, `Linear independence of monomials of multizeta values in positive characteristic,' preprint 1207.2326[NT].
  11. K. Joshi, `The t-motivic mixed Carlitz zeta category and Carlitz-Thakur multi-zeta values,' preprint 1306.2506[NT].
  12. Y. Mishiba, `Algebraic independence of the Carlitz period and the positive characteristic multizeta values at n and (n,n),' preprint 1307.3725[NT].
  13. J. A. Lara Rodríguez and D. Thakur, Zeta-like multizeta values for Fq[t],' preprint 1312.4928[NT].
  14. Y. Mishiba, `On algebraic independence of certain multizeta values in characteristic p,' preprint 1401.3628[NT].

E. ALTERNATING SERIES

  1. D. H. Bailey, J. M. Borwein, and R. Girgensohn, `Experimental evaluation of Euler sums,' Experiment. Math. 3 (1994), 17-30.
  2. D. Borwein, J. M. Borwein, and R. Girgensohn, `Explicit evaluation of Euler sums,' Proc. Edinburgh Math. Soc. 38 (1995), 277-294.
  3. V. Adamchik, `On Stirling numbers and Euler sums,' J. Comp. Appl. Math. 79 (1997), 119-130.
  4. 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.
  5. Wenchang Chu, `Hypergeometric series and the Riemann zeta function,' Acta Arithmetica 82 (1997), 103-118.
  6. P. Flajolet and B. Salvy, `Euler sums and contour integral representations,' Experiment. Math. 7 (1998), 15-35.
  7. 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.
  8. D. Borwein, J. M. Borwein, and D. M. Bradley, `Parametric Euler sum identities,' J. Math. Anal. Appl. 316 (2006), 328-338.
  9. J. M. Borwein and D. M. Bradley, `Thirty-two Goldbach variations,' Intl. J. Number Theory 2 (2006), 65-103; preprint NT/0502034.
  10. M. N. Lalín, `On a certain combination of colored multizeta values,' J. Ramanujan Math. Soc. 20 (2006), 115-127; preprint NT/0603442.
  11. J-Y. Enjalbert and Hoang Ngoc Minh, `Analytic and combinatoric aspects of Hurwitz polyzêtas', J. Théor. Nombres Bordeaux 19 (2007), 595-640.
  12. D-Y. Zheng, `Further summation formulae related to generalized harmonic numbers,' J. Math. Anal. Appl. 335 (2007), 692-706.
  13. 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.
  14. 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.
  15. 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].
  16. J. Zhao, `On a conjecture of Borwein, Bradley and Broadhurst,' J. reine angew. Math. 639 (2010), 223-233; cf. preprint 0705.2267[NT].
  17. 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].
  18. Z. Shen and T. Cai, `Some identities for alternating multiple zeta values' (Chinese), Acta Mathematica Sinica 56 (2013), 441-450.
  19. D. J. Broadhurst, `On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory,' preprint hep-th9604128.
  20. D. J. Broadhurst, `Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams,' preprint hep-th9612012.
  21. Z-h. Li, `On harmonic sums and alternating Euler sums,' preprint 1012.5192[NT].
  22. J. Zhao, `Restricted sum formula of alternating Euler sums,' preprint 1207.5366[NT].

F. MULTIPLE POLYLOGARITHMS/NESTED SUMS

  1. A. B. Goncharov, `Multiple polylogarithms, cyclotomy, and modular complexes,' Math. Res. Lett. 5 (1998), 497-516.
  2. 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.
  3. M. E. Hoffman, `Quasi-shuffle products,' J. Algebraic Combin. 11 (2000), 49-68; preprint.
  4. E. Remiddi and J. A. M. Vermaseren, `Harmonic polylogarithms,' Int. J. Modern Phys. A 15 (2000), 725-754; preprint hep-ph/9905237.
  5. A. B. Goncharov, `The dihedral Lie algebras and Galois symmetries of π1(l)( P1-({0,∞}∪μN)),' Duke Math. J. 110 (2001), 397-487; preprint AG/0009121.
  6. M. Yu. Kalmykov and O. Veretin, `Single scale diagrams and multiple binomial sums,' Phys. Lett. B 483 (2000), 315-323; preprint hep-th/0004010.
  7. 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.
  8. Hoang Ngoc Minh, M. Petitot, J. Van Der Hoeven, `Shuffle algebra and polylogarithms,' Discrete Math. 225 (2000), 217-230.
  9. 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.
  10. 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.
  11. J. M. Borwein, D. J. Broadhurst, and J. Kamnitzer, `Central binomial sums, multiple Clausen values, and zeta values,' Experiment. Math. 10 (2001), 25-34.
  12. 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).
  13. 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.
  14. G. Racinet, `Torseurs associés à certaines relations algébriques entre polyzêtas aux racines de l'unité,' C. R. Acad. Sci. Paris Ser. I 333 (2001), 5-10.
  15. G. Racinet, `Algèbre de Lie de valeuers formelles d'hyperlogarithmes aux racines de l'unité' C. R. Acad. Sci. Paris Ser. I 333 (2001), 11-16.
  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.
  17. 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.
  18. 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).
  19. 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.
  20. 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.
  21. M. Lalín, `Some examples of Mahler measure as multiple polylogarithms,' J. Number Theory 103 (2003), 85-108.
  22. E. A. Ulanskii, `Identities for generalized polylogarithms' (Russian), Mat. Zametki 73 (2003), 613-624; English translation in Math. Notes 73 (2003), 571-581.
  23. M. Kaneko and T. Arakawa, `On multiple L-values,' J. Math. Soc. Japan 56 (2004), 967-991.
  24. Hoang Ngoc Minh, `Shuffle algebra and differential Galois group of colored polylogarithms,' Nuclear Phys. B (Proc. Suppl.) 135 (2004), 220-224.
  25. J. Okuda, `Duality formulas of the special values of multiple polylogarithms,' Bull. London Math. Soc. 37 (2005), 230-242; preprint CA/0307137.
  26. J. Vollinga and S. Weinzierl, `Numerical evaluation of multiple polylogarithms,' Comput. Phys. Commun. 167 (2005), 177-194; preprint hep-ph/0410259.
  27. K. Matsumoto and H. Tsumura, `Generalized multiple Dirichlet series and generalized multiple polylogarithms,' Acta Arithmetica 124 (2006), 139-158.
  28. Q. Wang, `Moduli spaces and multiple polylogarithm motives,' Adv. in Math. 206 (2006), 329-357; preprint AG/0610670.
  29. 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.
  30. 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.
  31. 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).
  32. 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).
  33. 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).
  34. J. Zhao, `Analytic continuation of multiple polylogarithms,' Analysis Math. 33 (2007), 301-323; preprint AG/0302054.
  35. 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].
  36. J. Zhao, `Multiple polylogarithm values at roots of unity,' C. R. Acad. Sci. Paris Ser. I 346 (2008), 1029-1032; cf. preprint 0810.1064[NT].
  37. 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.
  38. N. Kurokawa, M. Lalín and H. Ochiai, `Higher Mahler measures and zeta functions,' Acta Arithmetica 135 (2008), 269-297; preprint 0908.0171[NT].
  39. 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].
  40. 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.
  41. Y. Yamasaki, `Evaluations of multiple Dirichlet L-values via symmetric functions,' J. Number Theory 129 (2009), 2369-2386; preprint 0712.1639[NT].
  42. T. Mansour, `Identities for sums of a q-analogue of polylogarithm functions,' Lett. Math. Phys. 87 (2009), 1-18.
  43. 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].
  44. J. Zhao, `Standard relations of multiple polylogarithms at roots of unity,' Documenta Math. 15 (2010), 1-34.
  45. A. Zaharescu and M. Zaki, `On the singularities of multiple L-functions,' Cent. Eur. J. Math. 8 (2010), 289-298.
  46. 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.
  47. 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].
  48. 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].
  49. S. Oi and K. Ueno, `Iterated integrals and relations of multiple polylogarithms,' in Representation Theory and Combinatorics, RIMS Kôkyûroku 1689 (2010), pp. 101-116.
  50. Y. Komori, K. Matsumoto, and H. Tsumura, `Multiple Bernoulli polynomials and multiple zeta-functions of root systems,' in Representation Theory and Combinatorics, RIMS Kôkyûroku 1689 (2010), pp. 117-132.
  51. 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.
  52. Y. Komori, K. Matsumoto, and H. Tsumura, `A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems,' RIMS Kôkyûroku Bessatsu B28 (2011), 99-120.
  53. 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.
  54. G. Kawashima, T. Tanaka, and N. Wakabayashi, `Cyclic sum formula for multiple L-values,' J. Algebra 348 (2011), 336-349.
  55. 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].
  56. 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].
  57. B. Enriquez and H. Furusho, `Mixed pentagon, octagon and Broadhurst duality equations,' J. Pure Appl. Algebra 216 (2012), 982-995.
  58. S. Zlobin, `Special values of generalized polylogarithms,' J. Math. Sci. 182 (2012), 484-504; preprint 0712.1656[NT].
  59. S. Oi and K. Ueno, `KZ equation on the moduli space M0,5 and the harmonic product of multiple polylogarithms,' Proc. London Math. Soc. (3) 105 (2012), 983-1020; preprint 0910.0718[QA].
  60. J. Enjalbert and Hoang Ngoc Minh, `Combinatorial study of colored Hurwitz polyzêtas,' Discrete Math. 312 (2012), 3489-3498; preprint 1206.1216[CO].
  61. 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.
  62. 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
  63. 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].
  64. 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].
  65. 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].
  66. K.-G. Schlesinger, `Some remarks on q-deformed multiple polylogarithms,' preprint QA/0111022.
  67. W. Zudilin, `One parameter models of Hopf algebras associated with multiple zeta values,' preprint.
  68. S. Oi, `Representaion of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta values,' preprint NT/0405162.
  69. S. Yamamoto, `A sum formula of multiple L-values,' preprint 1101.3948[NT].
  70. S. Oi and K. Ueno, `Connection problem of Knizhnik-Zamolodchikov equation on moduli space M0,5,' preprint 1109.0715[QA].
  71. H. Furusho, Y. Komori, K. Matsumoto, and H. Tsumura, `Desingularization of complex multiple zeta functions, fundamentals of p-adic multiple L-functions, and evaluation of their special values, preprint 1309.3982[NT].

G. FINITE MULTIPLE HARMONIC SUMS

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