AUTHOR INDEX

The author's name is linked to his or her profile on MathSciNet, if one exists.

[A] [B] [C] [D-E] [F] [G] [H] [I] [J] [K] [L] [M] [N] [O] [P] [R] [S] [T] [U] [V] [W] [X-Y] [Z]

A

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• J. Ablinger, Harmonic sums and polylogarithms generated by cyclotomic polynomials.
• V. Adamchik, On Stirling numbers and Euler sums.
• S. Akiyama,
  • Analytic continuation of multiple zeta-functions and their values at non-positive integers,
  • Multiple zeta values at non-positive integers,
  • On analytic continuation of multiple L-functions and related zeta functions.
• S. Albino, Analytic continuation of harmonic sums.
• G.W. Anderson, Multizeta values for F_q[t], their period interpretation, and relations between them.
• T. Aoki,
  • Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions,
  • A generating function for sums of multiple zeta values and its applications,
  • On generating functions of multiple zeta values and generalized hypergeometric functions.
• T. M. Apostol, Dirichlet series related to the Riemann zeta function.
• T. Arakawa,
  • Multiple zeta values, poly-Bernoulli numbers, and related zeta functions,
  • On multiple L-values.

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  B

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• D. H. Bailey, Experimental evaluation of Euler sums.
• A. Basu, A new method in the study of Euler sums.
• S. Baumard, Period polynomial relation between double zeta values.
• A. Besser, The double shuffle relations for p-adic multiple zeta values.
• M. Bigotte, Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables.
• J. Blümlein,
  • Harmonic sums and Mellin transforms up to two-loop order,
  • Analytic continuation of Mellin transforms up to two-loop order,
  • Algebraic relations between harmonic sums and associated quantities,
  • Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions,
  • Structural relations of harmonic sums and Mellin transforms at weight w=6,
  • Structural relations of harmonic sums and Mellin transforms up to weight w=5,
  • The multiple zeta value data mine,
  • Harmonic sums and polylogarithms generated by cyclotomic polynomials.
• J. Boersma, The evaluation of character Euler double sums.
• D. Borwein,
  • Explicit evaluation of Euler sums,
  • On an intriguing integral and some series related to ζ(4),
  • Parametric Euler sum identities.
• J. M. Borwein,
  • Experimental evaluation of Euler sums,
  • Explicit evaluation of Euler sums,
  • On an intriguing integral and some series related to ζ(4),
  • Evaluation of triple Euler sums,
  • Evaluation of k-fold Euler/Zagier sums: a compendium of results for arbitrary k,
  • Combinatorial aspects of multiple zeta values,
  • Special values of multidimensional polylogarithms,
  • Central binomial sums, multiple Clausen values, and zeta values,
  • Parametric Euler sum identities,
  • Thirty-two Goldbach variations,
  • Hilbert's inequality and Witten's zeta-function,
  • The evaluation of character Euler double sums,
  • Duality in tails of multiple zeta values.
• D. Bowman,
  • The algebra and combinatorics of shuffles and multiple zeta values,
  • Some multi-set inclusions associated with shuffle convolutions and multiple zeta values,
  • Resolution of some open problems concerning multiple zeta evaluations of arbitrary depth,
  • Multiple polylogarithms: a brief survey.
• K. N. Boyadzhiev,
  • Evaluation of Euler-Zagier sums,
  • Consecutive evaluation of Euler sums,
  • The values of an Euler sum at the negative integers and a relation to a certain convolution of Bernoulli numbers.
• D. M. Bradley,
  • Evaluation of k-fold Euler/Zagier sums: a compendium of results for arbitrary k,
  • Combinatorial aspects of multiple zeta values,
  • The algebra and combinatorics of shuffles and multiple zeta values,
  • Special values of multidimensional polylogarithms,
  • Multiple polylogarithms: a brief survey,
  • Some multi-set inclusions associated with shuffle convolutions and multiple zeta values.
  • Resolution of some open problems concerning multiple zeta evaluations of arbitrary depth,
  • Multiple q-zeta values,
  • Partition identities for the multiple zeta function,
  • A q-analog of Euler's decomposition formula for the double zeta function,
  • Duality for finite multiple harmonic q-series,
  • Parametric Euler sum identities,
  • Thirty-two Goldbach variations,
  • On the sum formula for multiple q-zeta values,
  • Signed q-analogs of Tornheim's double series,
  • A signed analog of Euler's reduction formula for the double zeta function,
  • Depth reduction of a class of Witten zeta functions,
  • On Mordell-Tornheim sums and multiple zeta values.
• D. J. Broadhurst,
  • Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops,
  • Evaluation of k-fold Euler/Zagier sums: a compendium of results for arbitrary k,
  • Massive 3-loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity,
  • Combinatorial aspects of multiple zeta values,
  • Special values of multidimensional polylogarithms,
  • Central binomial sums, multiple Clausen values, and zeta values,
  • On the enumeration of irreducible k-fold Euler sums and their roles in knot theory and field theory,
  • Conjectured enumeration of irreducible multiple zeta values, from knots and Feynman diagrams,
  • The multiple zeta value data mine.
• F. C. S. Brown,
  • Multiple zeta values and periods of moduli spaces M_0,n,
  • Périodes des espaces des modules M_0,n et valeuers zêtas multiples,
  • The massless higher-loop two-point function,
  • Algebra of cell-zeta values,
  • On the decomposition of motivic multiple zeta values,
  • Mixed Tate motives over Z.
• J. P. Buhler, On the evaluation of Euler sums.

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  C

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• T. Cai,
  • Signed q-analogs of Tornheim's double series,
  • Depth reduction of a class of Witten zeta functions,
  • Some identities for multiple zeta values.
• B. Candelpergher, The Arakawa-Kaneko zeta function.
• S. Carr,
  • Periods on the moduli space of genus 0 curves,
  • Algebra of cell-zeta values.
• P. Cartier,
  • Fonctions polylogarithmes, nombres polyzêtas et groupes pro-unipotents,
  • On the double zeta values.
• O-Y. Chan, Duality in tails of multiple zeta values.
• K-W. Chen, Explicit evaluations of extended Euler sums.
• Y-H. Chen, Multiple zeta values and application to the Lacunary recurrence formulas of Bernoulli numbers.
• Y. J. Cho, Euler sums evaluatable from integrals.
• J. Choi,
  • Euler sums evaluatable from integrals,
  • Explicit evaluation of Euler and related sums,
  • Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals.
• M. W. Coffey,
  • On some log-cosine integrals related to ζ(3), ζ(4), and ζ(6),
  • On one-dimensional digamma and polygamma series related to the evaluation of Feynman digrams,
  • On a three-dimensional symmetric Ising tetrahedron and contributions to the theory of the dilogarithm and Clausen functions.
• M-A. Coppo,
  • Sur les sommes d'Euler divergentes,
  • The Arakawa-Kaneko zeta function.
• C. Costermans,
  • Algorithmic and combinatoric aspects of multiple harmonic sums,
  • Structure and asymptotic expansion of multiple harmonic sums,
  • Some results à l'Abel obtained by use of techniques à la Hopf,
  • Noncommutative algebra, multiple harmonic sums and applications in discrete probability.
• R. E. Crandall,
  • On the evaluation of Euler sums,
  • Fast evaluation of multiple zeta sums.
• J. Cresson,
  • Polyzétas stricts, larges et pondérés,
  • Séries hypergéometriques multiples et polyzêtas,
  • Phénomènes de symétrie dans des formes linéaires en polyzêtas.

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  D-E

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• A. I. Davydychev,
  • Some remarks on the ε-expansion of dimensionally regulated Feynman diagrams,
  • New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams,
  • Massive Feynman diagrams and inverse binomial sums.
• M. de Crisenoy,
  • Values at T-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables,
  • Relations between values at T-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables.
• K. Ebrahimi-Fard, Multiple zeta values and Rota-Baxter algebras.
• J. Écalle,
  • ARI/GARI, la dimorphie et l'arithmétique des multizêtas: un premier bilan,
  • Recent advances in the analysis of divergence and singularities,
  • Multizetas, perinomal numbers, arithmetical dimorphy, and ARI/GARI.
• S. Egami, Analytic continuation of multiple zeta-functions and their values at non-positive integers.
• M. Eie,
  • Explicit evaluations of extended Euler sums,
  • Explicit evaluation of triple Euler sums,
  • A short proof of the sum formula and its generalization,
  • Double Euler sums on Hurwitz zeta functions,
  • A restricted sum formula among multiple zeta values,
  • Topics in Number Theory,
  • Explicit evaluations of quadruple Euler sums.
  • Some alternating double sum formulae of multiple zeta values.
• J-Y. Enjalbert,
  • Analytic and combinatoric aspects of Hurwitz polyzêtas,
  • Algorithmic and combinatoric aspects of multiple harmonic sums,
  • Structure and asymptotic expansion of multiple harmonic sums.
• B. Enriquez, A formula for the logarithm of the KZ associator.
• M. Espie, Formal computations about multiple zeta values.
• O. Espinosa,
  • The evaluation of Tornheim double sums, Part I,
  • The evaluation of Tornheim double sums, Part II.
• D. Essouabri,
  • Relations between values at T-tuples of negative integers of twisted multivariable zeta series associated to polynomials of several variables.
  • Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula.
• L. Euler, Meditationes circa singulare serierum genus.

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  F

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• S. Fischler,
  • Formes linéaires en polyzêtas et intégrales multiples,
  • Séries hypergéometriques multiples et polyzêtas,
  • Phénomènes de symétrie dans des formes linéaires en polyzêtas,
  • Multiple series connected to Hoffman's conjecture on multiple zeta values.
• P. Flajolet, Euler sums and contour integral representations.
• P. Freitas, Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums.
• H. Furusho,
  • The multiple zeta value algebra and the stable derivation algebra,
  • p-Adic multiple zeta values I--p-adic multiple polylogarithms and the p-adic KZ equation,
  • The double shuffle relations for p-adic multiple zeta values,
  • Multiple zeta values and Grothendick-Teichmüller groups,
  • p-Adic multiple zeta values II--Tannakian interpretations,
  • Regularization and generalized double shuffle relations for p-adic multiple zeta values,
  • Double shuffle relation for associators.
• J. Furuya, Analytic properties of Dirichlet series obtained from the error term in the Dirichlet divisor problem.
• P. H. Fuss (ed.), Correspondance Mathématique et Physique de quelques célèbres Géomètres.

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  G

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• H. G. Gadiyar, The values of an Euler sum at the negative integers and a relation to a certain convolution of Bernoulli numbers.
• H. Gangl, Double zeta values and modular forms.
• F. Gavarini, A formula for the logarithm of the KZ associator.
• R. Girgensohn,
  • Experimental evaluation of Euler sums,
  • Explicit evaluation of Euler sums,
  • Evaluation of triple Euler sums.
• A. B. Goncharov,
  • Multiple polylogarithms, cyclotomy, and modular complexes,
  • The dihedral Lie algebras and Galois symmetries of π₁^(l)(P¹-({0,∞} ∪μ_N)),
  • Multiple ζ-values, Galois groups, and geometry of modular varieties,
  • Multiple ζ-motives and moduli spaces M_0,n.
• A. Granville, A decomposition of Riemann's zeta-function.
• P. Guha, Witten's volume formula, cohomological pairings of moduli spaces of flat connections and applications of multiple zeta functions.
• S. Gun, On a conjecture of Chowla and Milnor.
• L. Guo,
  • Multiple zeta values and Rota-Baxter algebras,
  • Renormalization of multiple zeta values,
  • Differential Algebraic Birkhoff Decomposition and the renormalization of multiple zeta values,
  • Algebraic Birkhoff decomposition and its applications,
  • Explicit double shuffle relations and a generalization of Euler's decomposition formula,
  • Weighted sum formulas for multiple zeta values,
  • Double shuffle relations and renormalization of multiple zeta values,
  • Polylogarithms and multiple zeta values from free Rota-Baxter algebras,
  • The shuffle relation of fractions from multiple zeta values.

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  H

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• Kh. Hessami Pilehrood, Congruences arising from Apéry-type series for zeta values.
• T. Hessami Pilehrood, Congruences arising from Apéry-type series for zeta values.
• Hoang Ngoc Minh,
  • Computation of the monodromy of generalized polylogarithms,
  • Aspects combinatoires des polylogarithms et des sommes d'Euler-Zagier,
  • Lyndon words, polylogarithms, and the Riemann ζ function,
  • De l'algèbre des ζ de Riemann multivariées à l'algèbre des ζ de Hurwitz multivariées,
  • Shuffle algebra and differential Galois group of colored polylogarithms,
  • Analytic and combinatoric aspects of Hurwitz polyzêtas,
  • Algorithmic and combinatoric aspects of multiple harmonic sums,
  • Structure and asymptotic expansion of multiple harmonic sums,
  • Some results à l'Abel obtained by use of techniques à la Hopf,
  • Noncommutative algebra, multiple harmonic sums and applications in discrete probability.
• M. E. Hoffman,
  • Multiple harmonic series,
  • Sums of triple harmonic series,
  • The algebra of multiple harmonic series,
  • Quasi-shuffle products,
  • Periods of mirrors and multiple zeta values,
  • Relations of multiple zeta values and their algebraic expression,
  • Algebraic aspects of multiple zeta values,
  • The Hopf algebra structure of multiple harmonic sums,
  • Quasi-symmetric functions, multiple zeta values, and rooted trees,
  • A character on the quasi-symmetric functions coming from multiple zeta values,
  • Quasi-symmetric functions and mod p multiple harmonic sums.
• I. Horozov, Multiple zeta values, modular forms, and adeles.
• J. G. Huard, On Tornheim's double series.

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  I

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• M. Igarashi,
  • Cyclic sum of certain parametrized multiple series,
  • A generalization of Ohno's relation for multiple zeta values,
  • Note on relations among multiple zeta-star values,
  • On generalizations of the sum formula for multiple zeta values.
• K. Ihara,
  • The quantum g2 invariant and relations of multiple zeta values,
  • Derivation and double shuffle relations for multiple zeta values,
  • Symmetry on linear relations for multiple zeta values.
  • Multiple zeta values vs. multiple zeta star values.
• K. Imatomi, On some combinations of multiple zeta-star values.
• H. Ishikawa,
  • On analytic continuation of multiple L-functions and related zeta functions,
  • On the estimation of the order of Euler-Zagier multiple zeta-functions.

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  J

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• G. Jacob,
  • Aspects combinatoires des polylogarithms et des sommes d'Euler-Zagier,
  • Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables,
  • De l'algèbre des ζ de Riemann multivariées à l'algèbre des ζ de Hurwitz multivariées.
• A. Jafari, Regularization and generalized double shuffle relations for p-adic multiple zeta values.
• D. S. Jang, Explicit evaluations of special multiple zeta values ζ({4l+2}_n) and ζ({4l}_n).
• M. Jung, Euler sums evaluatable from integrals.

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  K

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• J. Kajikawa,
  • Duality and double shuffle relations for multiple zeta values,
  • Multiple zeta values vs. multiple zeta star values.
• M. Yu. Kalmykov,
  • Single scale diagrams and multiple binomial sums,
  • Some remarks on the ε-expansion of dimensionally regulated Feynman diagrams,
  • New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams,
  • Massive Feynman diagrams and inverse binomial sums,
  • All order ε-expansion of Gauss hypergeometric functions with integer or half-integer values of parameters,
  • 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,
  • On the all-order ε-expansion of generalized hypergeometric functions with integer values of parameters,
  • Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters,
  • "Sixth root of unity" and Feynman diagrams: hypergeometric function approach point of view.
• K. Kamano, The multiple Hurwitz zeta function and a generalization of Lerch's formula.
• J. Kamnitzer, Central binomial sums, multiple Clausen values, and zeta values.
• M. Kaneko,
  • Multiple zeta values, poly-Bernoulli numbers, and related zeta functions,
  • On multiple L-values,
  • Multiple zeta values,
  • Double zeta values and modular forms,
  • Derivation and double shuffle relations for multiple zeta values,
  • On an extension of the derivation relation for multiple zeta values,
  • A note on poly-Bernoulli numbers and multiple zeta values,
  • On a conjecture for the dimension of the space of the multiple zeta values,
  • Poly-Bernoulli numbers and related zeta functions,
  • On a kind of duality of multiple zeta-star values.
• G. Kawashima,
  • A class of relations among multiple zeta values,
  • A generalization of the duality for multiple harmonic sums,
  • Multiple series expressions for the Newton series which interpolate finite multiple harmonic sums.
  • A generalization of the duality for finite multiple harmonic q-series.
• J. P. Kelliher, Analytic continuation of multiple Hurwitz zeta functions.
• K. Kimoto, A variation of multiple L-values arising from the spectal zeta function of the non-commutative harmonic oscillator.
• S. Kitani, Finite automata and relations of multiple zeta values.
• I. Kiuchi,
  • Bounds for double zeta-functions,
  • Bounds for triple zeta-functions,
  • Analytic properties of double zeta-functions.
• B. A. Kniehl,
  • Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters,
  • "Sixth root of unity" and Feynman diagrams: hypergeometric function approach point of view.
• Y. Kombu, A generating function for sums of multiple zeta values and its applications.
• Y. Komori,
  • Zeta functions of root systems,
  • An integral representation of the Mordell-Tornheim double zeta function and its values at non-positive integers,
  • Zeta and L-functions and Bernoulli polynomials of root systems,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras II,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras III,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras IV,
  • Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems,
  • Functional relations for zeta-functions of root systems,
  • An introduction to the theory of zeta-functions of root systems,
  • Multiple Bernoulli polynomials and multiple zeta-functions of root systems,
  • On multiple Bernoulli polynomials and multiple L-functions of root systems,
  • Multiple zeta values and zeta-functions of root systems,
  • A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems.
• H. Kondo, The Bowman-Bradley theorem for multiple zeta-star values.
• M. Kontsevich, Periods.
• D. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops.
• M. Kuba,
  • On evaluations of infinte double series and Tornheim's double series,
  • On functions of Arakawa and Kaneko and multiple zeta functions,
  • Generalized reciprocity laws for sums of multiple harmonic numbers,
  • On a reciprocity law for finite multiple zeta values,
  • A note on Stirling series.
• J. Kuipers, About a conjectured basis for multiple zeta values.
• N. Kurokawa, Higher Mahler measure and zeta functions.
• S. Kurth, Harmonic sums and Mellin transforms up to two-loop order.

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  L

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• M. N. Lalín,
  • Some examples of Mahler measure as multiple polylogarithms,
  • On a certain combination of colored multizeta values,
  • Higher Mahler measure and zeta functions.
• J. A. Lara Rodríguez,
  • Some conjectures and results about multiple zeta values over F_q[t],
  • Relations between multizeta values in characteristic p,
  • Special relations between multizeta values and parity results.
• T. Q. T. Lê,
  • Kontsevich's integral for the Homfly polynomial and relations between values of the multiple zeta functions,
  • Kontsevich's integral for the Kauffman polynomial.
• Z-h. Li,
  • Sum of multiple zeta values of fixed weight, depth and i-height,
  • Sum of multiple q-zeta values,
  • Gamma series associated to elements satisfying regularized double shuffle relations,
  • Higher order shuffle regularization for multiple zeta values,
  • On functional relations for the alternating analogues of Tornheim's double zeta function,
  • On harmonic sums and alternating Euler sums,
  • On a conjecture of Kaneko and Ohno.
• W-C. Liaw,
  • Explicit evaluation of triple Euler sums,
  • A restricted sum formula among multiple zeta values,
  • Double Euler sums on Hurwitz zeta functions.
• P. Lisoněk,
  • Combinatorial aspects of multiple zeta values,
  • Special values of multidimensional polylogarithms.
• R. Lu, The Γ^-genus and a regularization of an S¹-equivariant Euler class.

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  M

  ---

• T. Machide,
  • Generators for vector spaces consisting of double zeta values with even weight,
  • Weighted sums with two parameters of multiple zeta values and their formulas.
• D. Manchon,
  • Nested sums of symbols and renormalised multiple zeta functions,
  • Renormalized multiple zeta values which respect quasi-shuffle relations.
• Yu. I. Manin,
  • Iterated integrals of modular forms and noncommutative modular symbols,
  • Multiple ζ-motives and moduli spaces M_0,n.
• T. Mansour, Identities for sums of a q-analogue of polylogarithm functions.
• C. Markett, Triple sums and the Riemann zeta function.
• R. Masri,
  • The Herglotz-Zagier function, double zeta values, and values of L-series,
  • Multiple Dedekind zeta functions and evaluations of extended multiple zeta values,
  • Analytic continuation of multiple Hurwitz zeta functions,
  • Multiple zeta values over global function fields.
• O. Mathieu, On a symmetric space attached to polyzeta values.
• K. Matsumoto,
  • On the analytic continuation of various multiple-zeta functions,
  • On Mordell-Tornheim and other multiple zeta-functions,
  • The analytic continuation and the asymptotic behavior of certain multiple zeta-functions I,
  • The analytic continuation and the asymptotic behavior of certain multiple zeta-functions II,
  • On the estimation of the order of Euler-Zagier multiple zeta-functions,
  • Functional equations for double zeta-values,
  • The analytic continuation and the asymptotic behavior of certain multiple zeta-functions III,
  • Generalized multiple Dirichlet series and generalized multiple polylogarithms,
  • Analytic properties of multiple zeta-functions in several variables,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras I,
  • Zeta functions of root systems,
  • Functional relations and special values of Mordell-Tornheim triple and L-functions,
  • A new method of producing functional relations among multiple zeta-functions,
  • On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions,
  • Functional relations among certain double polylogarithms and their character analogues,
  • Zeta and L-functions and Bernoulli polynomials of root systems,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras II,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras III,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras IV,
  • Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems,
  • Functional relations for zeta-functions of root systems,
  • An introduction to the theory of zeta-functions of root systems,
  • The analytic theory of multiple zeta-fucntions of root systems,
  • Multiple Bernoulli polynomials and multiple zeta-functions of root systems,
  • On multiple Bernoulli polynomials and multiple L-functions of root systems,
  • Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula,
  • Multiple zeta values and zeta-functions of root systems,
  • A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems.
• S. Moch,
  • Nested sums, expansion of transcendental functions and multiscale multiloop integrals,
  • Deep inelastic structure functions at two loops,
  • Analytic continuation of the harmonic sums for the 3-loop anomalous dimensions.
• C. Moen, Sums of triple harmonic series.
• V. H. Moll,
  • The evaluation of Tornheim double sums, Part I,
  • The evaluation of Tornheim double sums, Part II.
• U. Müller, A quantum field theoretical representation of Euler-Zagier sums.
• S. Muneta,
  • On some explicit evaluations of multiple star-zeta values,
  • Algebraic setup of non-strict multiple zeta values,
  • A note on evaluations of multiple zeta values.
• J. Murakami,
  • Kontsevich's integral for the Homfly polynomial and relations between values of the multiple zeta functions,
  • Kontsevich's integral for the Kauffman polynomial.
• M. Ram Murty,
  • Multiple Hurwitz zeta functions ,
  • On a conjecture of Chowla and Milnor.

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  N

  ---

• T. Nakamura,
  • Bernoulli numbers and multiple zeta values,
  • A functional relation for the Tornheim zeta function,
  • Functional relations and special values of Mordell-Tornheim triple zeta and L-functions,
  • On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions,
  • Zeroes and the universality for the Euler-Zagier-Hurwitz type of multiple zeta-functions,
  • Double Lerch series and their functional relations,
  • Restricted and weighted sum formulas for double zeta values of even weight,
  • Simple proof of the functional relation for the Lerch type Tornheim double zeta function,
  • Applications of hybrid universality to multivariable zeta-functions.
• N. Nielsen, Die Gammafunktion.
• J-C. Novelli, Formal computations about multiple zeta values.
• M. Noro, On a conjecture for the dimension of the space of the multiple zeta values.

  ---

  O

  ---

• H. Ochiai,
  • Symmetry on linear relations for multiple zeta values,
  • On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions,
  • Higher Mahler measure and zeta functions.
• Y. Ohno,
  • A generalization of the duality and sum formulas on the multiple zeta values,
  • Multiple zeta values of fixed weight, depth, and height,
  • Relations of multiple zeta values and their algebraic expression,
  • Sum relations for multiple zeta values,
  • Sum relations for multiple zeta values and connection formulas for the Gauss hypergeometric functions,
  • Cyclic sum of multiple zeta values,
  • On the sum formula for the q-analogue of non-strict multiple zeta values,
  • A generating function for sums of multiple zeta values and its applications,
  • Zeta stars,
  • Cyclic q-MZSV sum,
  • On generating functions of multiple zeta values and generalized hypergeometric functions,
  • Multiple zeta values vs. multiple zeta star values,
  • On a kind of duality of multiple zeta-star values.
• S. Oi,
  • Representation of the Gauss hypergeometric function by multiple polylogarithms and relations of multiple zeta values,
  • Gauss hypergeometric functions, multiple polylogarithms, and multiple zeta values,
  • The formal KZ equation of the moduli space M_0,5 and the harmonic product of multiple zeta values,
  • Iterated integrals and relations of multiple polylogarithms,
  • Connection property of Knizhnik-Zamolodchikov equation on moduli space M_0,5.
• J. Okuda,
  • Relations for multiple zeta values and Mellin transforms of multiple polylogarithms,
  • The sum formula for multiple zeta values and connection problem of the formal Knizhnik-Zamolodchikov equation,
  • Duality formulas of the special values of multiple polylogarithms,
  • On the sum formula for the q-analogue of non-strict multiple zeta values,
  • On relations for the multiple q-zeta values,
  • New approach to Ohno relations for multiple zeta values,
  • Cyclic q-MZSV sum,
  • Multiple zeta values vs. multiple zeta star values.
• Y. L. Ong,
  • Explicit evaluation of triple Euler sums,
  • A restricted sum formula among multiple zeta values,
  • Explicit evaluations of quadruple Euler sums,
  • Some alternating double sum formulae of multiple zeta values.
• K. Onodera, Generalized log sine integrals and the Mordell-Tornheim zeta values.
• N. E. Oussous,
  • Aspects combinatoires des polylogarithms et des sommes d'Euler-Zagier,
  • Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables,
  • De l'algèbre des ζ de Riemann multivariées à l'algèbre des ζ de Hurwitz multivariées.

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  P

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• R. Padma, The values of an Euler sum at the negative integers and a relation to a certain convolution of Bernoulli numbers.
• A. Panholzer, Computer-free evaluation of an infinite double sum via Euler sums.
• Ł. Pańkowski, Applications of hybrid universality to multivariable zeta-functions.
• S. Paycha,
  • Double shuffle relations and renormalization of multiple zeta values,
  • Nested sums of symbols and renormalised multiple zeta functions.
• R. Pemantle, When is 0.999... equal to 1?.
• A. Petojević, Computation of the Mordell-Tornheim zeta values.
• M. Petitot,
  • Computation of the monodromy of generalized polylogarithms,
  • Aspects combinatoires des polylogarithms et des sommes d'Euler-Zagier,
  • Lyndon words, polylogarithms, and the Riemann ζ function,
  • Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables,
  • De l'algèbre des ζ de Riemann multivariées à l'algèbre des ζ de Hurwitz multivariées,
  • Structure and asymptotic expansion of multiple harmonic sums.
• H. Prodinger,
  • Computer-free evaluation of an infinite double sum via Euler sums,
  • Generalized reciprocity laws for sums of multiple harmonic numbers,
  • On a reciprocity law for finite multiple zeta values.
  • A note on Stirling series.

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  R

  ---

• G. Racinet,
  • Torseurs associés à certaines relations algébriques entre polyzêtas aux racines de l'unité,
  • Algèbre de Lie de valeuers formelles d'hyperlogarithmes aux racines de l'unité,
  • Formal computations about multiple zeta values,
  • Doubles mélanges des polylogarithmes multiples aux racines de l'unité.
• T. M. Rassias, Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers.
• P. Rath, On a conjecture of Chowla and Milnor.
• E. Remiddi, Harmonic polylogarithms.
• T. Rivoal,
  • Séries hypergéometriques multiples et polyzêtas,
  • Phénomènes de symétrie dans des formes linéaires en polyzêtas,
  • Hypergeometric constructions of rational approximations for (multiple) zeta values.
• J. H. Ryoo, Some multi-set inclusions associated with shuffle convolutions and multiple zeta values

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  S

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• S. Saito,
  • The Bowman-Bradley theorem for multiple zeta-star values,
  • Combinatorial remarks on the cyclic sum theorem for multiple zeta values.
• B. Salvy, Euler sums and contour integral representations.
• Y. Sasaki,
  • Multiple zeta values for coordinatewise limits at non-positive integers,
  • The first derivative multiple zeta values at non-positive integers.
• E. Sawada, Finite automata and relations of multiple zeta values.
• K.-G. Schlesinger, Some remarks on q-deformed multiple polylogarithms.
• C. Schneider,
  • When is 0.999... equal to 1?,
  • Generalized reciprocity laws for sums of multiple harmonic numbers,
  • Harmonic sums and polylogarithms generated by cyclotomic polynomials.
• L. Schneps,
  • Algebra of cell-zeta values,
  • Period polynomial relation between double zeta values,
  • Double shuffle and Kashiwara-Vergne Lie algebras.
• C. Schubert, A quantum field theoretical representation of Euler-Zagier sums.
• C. Sekine, Partial sums of multiple zeta value series.
• L-C. Shen, Remarks on some integrals and series involving the Stirling numbers and ζ(n).
• Z. Shen, Some identities for multiple zeta values.
• K. Sinha, Multiple Hurwitz zeta functions.
• R. Sitaramachandrarao,
  • On some infinite series of L. J. Mordell and their analogues,
  • Transformation formulae for multiple series.
• J-W. Son, Explicit evaluations of special multiple zeta values ζ({4l+2}_n) and ζ({4l}_n).
• J. Sondow, Integrals over polytopes, multiple zeta values and polylogarithms, and Euler's constant.
• I. Soudères,
  • Motivic double shuffle,
  • Explicit associator relations for multiple zeta values.
• H. M. Srivastava,
  • Some classes of infinite series associated with the Riemann zeta and polygamma functions and generalized harmonic numbers,
  • Explicit evaluation of Euler and related sums,
  • Computation of the Mordell-Tornheim zeta values,
  • Some applications of the Gamma and polygamma functions involving convolutions of the Rayleigh functions, multiple Euler sums and log-sine integrals.
• M. V. Subbarao,
  • On some infinite series of L. J. Mordell and their analogues,
  • Transformation formulae for multiple series.

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  T

  ---

• T. Takamuki,
  • The Kontsevich invariant and relations of multiple zeta values,
  • The quantum g2 invariant and relations of multiple zeta values.
• Y. Takeyama,
  • On relations for the multiple q-zeta values,
  • A q-analogue of non-strict multiple zeta values and basic hypergeometric series,
  • Quadratic relations for a q-analogue of multiple zeta values.
  • A restricted sum formula for a q-analogue of multiple zeta values
• T. Tanaka,
  • On the quasi-derivation relation for multiple zeta values,
  • An algebraic proof of cyclic sum formula for multiple zeta values,
  • On some combinations of multiple zeta-star values,
  • The Bowman-Bradley theorem for multiple zeta-star values,
  • Combinatorial remarks on the cyclic sum theorem for multiple zeta values.
• Y. Tanigawa,
  • Analytic continuation of multiple zeta-functions and their values at non-positive integers,
  • Multiple zeta values at non-positive integers,
  • Bounds for double zeta-functions,
  • Bounds for triple zeta-functions,
  • Analytic properties of Dirichlet series obtained from the error term in the Dirichlet divisor problem,
  • Analytic properties of double zeta-functions .
• K. Tasaka,
  • On some combinations of multiple zeta-star values,
  • On some multiple zeta-star values of one-two-three indices.
• R. Tauraso,
  • Congruences involving multiple harmonic sums,
  • New harmonic number identities with applications,
  • Congruences of alternating multiple harmonic sums.
• T. Terasoma,
  • Selberg integrals and multiple zeta values,
  • Mixed Tate motives and multiple zeta values,
  • Geometry of multiple zeta values,
  • Period integrals and multiple zeta values.
• D. Terhune,
  • Evaluation of double L-values,
  • Evaluations of a class of double L-values.
• D. Thakur,
  • Function Field Arithmetic,
  • Multizeta values for F_q[t], their period interpretation, and relations between them,
  • Relations between multizeta values for F_q[t],
  • Power sums with applications to multizeta and zeta zero distribution for F_q[t],
  • Shuffle relations for function field multiple zeta values.
• L. Tornheim, Harmonic double series.
• H. Tsumura,
  • On some combinatorial relations for Tornheim's double series,
  • On alternating analogues of Tornheim's double series,
  • Evaluation formulas for Tornheim's type of alternating double series,
  • On evaluation formulas for double L-values,
  • Combinatorial relations for Euler-Zagier sums,
  • Multiple harmonic series related to multiple Euler numbers,
  • On Mordell-Tornheim zeta values,
  • Certain functional relations for the double harmonic series related to the double Euler numbers,
  • On some functional relations between Mordell-Tornheim double L-functions and Dirichlet L-functions,
  • Generalized multiple Dirichlet series and generalized multiple polylogarithms,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras I,
  • Zeta functions of root systems,
  • On functional relations between the Mordell-Tornheim double zeta functions and the Riemann zeta function,
  • Functional relations and special values of Mordell-Tornheim triple and L-functions,
  • A new method of producing functional relations among multiple zeta-functions,
  • On value-relations, functional relations and singularities of Mordell-Tornheim and related triple zeta-functions,
  • Functional relations among certain double polylogarithms and their character analogues,
  • Zeta and L-functions and Bernoulli polynomials of root systems,
  • On alternating analogues of Tornheim's double series II,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras II,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras III,
  • On Witten multiple zeta-functions associated with semisimple Lie algebras IV,
  • Shuffle products for multiple zeta values and partial fraction decompositions of zeta-functions of root systems,
  • Functional relations for zeta-functions of root systems,
  • An introduction to the theory of zeta-functions of root systems,
  • Multiple Bernoulli polynomials and multiple zeta-functions of root systems,
  • On multiple Bernoulli polynomials and multiple L-functions of root systems,
  • Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula,
  • Multiple zeta values and zeta-functions of root systems,
  • A survey on the theory of multiple Bernoulli polynomials and multiple L-functions of root systems.
• K. Tsurumaki, On a conjecture for the dimension of the space of the multiple zeta values.

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  U

  ---

• K. Ueno,
  • Relations for multiple zeta values and Mellin transforms of multiple polylogarithms,
  • The sum formula for multiple zeta values and connection problem of the formal Knizhnik-Zamolodchikov equation,
  • New approach to Ohno relations for multiple zeta values,
  • Finite automata and relations of multiple zeta values,
  • The formal KZ equation of the moduli space M_0,5 and the harmonic product of multiple zeta values,
  • Iterated integrals and relations of multiple polylogarithms,
  • Connection property of Knizhnik-Zamolodchikov equation on moduli space M_0,5.
• E. A. Ulanskii,
  • Identities for generalized polylogarithms,
  • Stuffle relations for multiple zeta values.
  • Multiple zeta values.
• S. Ünver, p-Adic multi-zeta values.
• P. Uwer, Nested sums, expansion of transcendental functions and multiscale multiloop integrals.

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  V

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• J. Van Der Hoven, Computation of the monodromy of generalized polylogarithms.
• O. Veretin, Single scale diagrams and multiple binomial sums.
• J. A. M. Vermaseren,
  • Harmonic sums, Mellin transforms and integrals,
  • Harmonic polylogarithms,
  • Deep inelastic structure functions at two loops,
  • The multiple zeta value data mine,
  • About a conjectured basis for multiple zeta values.
• R-O. Vîlceanu, The multiple zeta function and the computation of some integrals in compact form.
• J. Vollinga, Numerical evaluation of multiple polylogarithms.
• T. H. Vu, Dirichlet series related to the Riemann zeta function.

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  W

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• N. Wakabayashi,
  • Cyclic sum of multiple zeta values,
  • An algebraic proof of cyclic sum formula for multiple zeta values,
  • On some combinations of multiple zeta-star values,
  • Combinatorial remarks on the cyclic sum theorem for multiple zeta values,
  • On generating functions of multiple zeta values and generalized hypergeometric functions.
• M. Waldschmidt,
  • Valeurs zêta multiples. Une introduction,
  • Hopf algberas and transcendental numbers,
  • Multiple polylogarithms: an introduction.
• Q. Wang, Moduli spaces and multiple polylogarithm motives.
• B. F. L. Ward,
  • All order ε-expansion of Gauss hypergeometric functions with integer or half-integer values of parameters,
  • 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,
  • On the all-order ε-expansion of generalized hypergeometric functions with integer values of parameters.
• C-S. Wei,
  • A short proof of the sum formula and its generalization,
  • Explicit evaluations of quadruple Euler sums.
• S. Weinzierl,
  • Nested sums, expansion of transcendental functions and multiscale multiloop integrals,
  • Numerical evaluation of multiple polylogarithms.
• Chu Wenchang, Symmetric functions and the Riemann zeta series.
• G. T. Williams, A new method of evaluating ζ(2n).
• K. S. Williams, On Tornheim's double series.

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  X-Y

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• B. Xie,
  • Explicit double shuffle relations and a generalization of Euler's decomposition formula,
  • Weighted sum formulas for multiple zeta values,
  • Double shuffle relations and renormalization of multiple zeta values,
  • The shuffle relation of fractions from multiple zeta values.
• S. Yamamoto,
  • A sum formula of multiple L-values,
  • Explicit evaluations of certain sums of multiple zeta-star values,
  • On some multiple zeta-star values of one-two-three indices,
  • Interpolation of multiple zeta and zeta-star values.
• Y. Yamasaki,
  • A variation of multiple L-values arising from the spectal zeta function of the non-commutative harmonic oscillator,
  • Evaluations of multiple Dirichlet L-values via symmetric functions.
• C. Yamazaki, On the duality for multiple star-zeta vales of height one.
• F-Y. Yang, Some alternating double sum formulae of multiple zeta values.
• A. J. Yee, A new shuffle convolution for multiple zeta values.
• S. Yost,
  • All order ε-expansion of Gauss hypergeometric functions with integer or half-integer values of parameters,
  • 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,
  • On the all-order ε-expansion of generalized hypergeometric functions with integer values of parameters.

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  Z

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• D. Zagier,
  • Values of zeta functions and their applications,
  • Periods,
  • Multiple zeta values of fixed weight, depth, and height,
  • Double zeta values and modular forms,
  • Derivation and double shuffle relations for multiple zeta values,
  • Evaluation of the multiple zeta values ζ(2,...,2,3,2,...,2).
• A. Zaharescu, On the singularities of multiple L-functions.
• M. Zaki, On the singularities of multiple L-functions.
• M. Zakrzewski,
  • Linear differential equations and multiple zeta values I. Zeta(2),
  • Linear differential equations and multiple zeta values II. A generalization of the WKB method.
• W. Zhai, Analytic properties of double zeta-functions.
• B. Zhang,
  • Renormalization of multiple zeta values,
  • Differential Algebraic Birkhoff Decomposition and the renormalization of multiple zeta values,
  • Double shuffle relations and renormalization of multiple zeta values,
  • Polylogarithms and multiple zeta values from free Rota-Baxter algebras.
• N-Y. Zhang, On Tornheim's double series.
• J. Zhao,
  • Analytic continuation of multiple zeta functions,
  • Multiple q-zeta functions and multiple q-polylogarithms,
  • Bernoulli numbers, Wolstenholme's theorem, and p⁵ variations of Lucas' theorem,
  • Wolstenholme type theorem for multiple harmonic sums,
  • Analytic continuation of multiple polylogarithms,
  • Multiple harmonic sums II: Finiteness of p-divisible sets,
  • Renormalization of multiple q-zeta values,
  • An exotic shuffle relation for multiple zeta values,
  • Multiple polylogarithm values at roots of unity,
  • Standard relations of multiple polylogarithms at roots of unity,
  • Reducibility of signed cyclic sums of Mordell-Tornheim zeta and L-values,
  • Alternating Euler sums and special values of Witten multiple zeta function attached to so(5),
  • Witten multiple zeta values attached to sl(4),
  • Multi-polylogs at twelfth roots of unity and special values of Witten multiple zeta function attached to the exceptional Lie algebra g₂,
  • A note on colored Tornheim's double series,
  • On a conjecture of Borwein, Bradley and Broadhurst,
  • Witten volume formulas for semi-simple Lie algebras,
  • Congruences of alternating multiple harmonic sums,
  • Mod p structure of alternating and non-alternating multiple harmonic sums.
• D-Y. Zheng, Further summation formulae related to generalized harmonic numbers.
• X. Zhou,
  • Signed q-analogs of Tornheim's double series,
  • Reducibility of signed cyclic sums of Mordell-Tornheim zeta and L-values,
  • Witten multiple zeta values attached to sl(4),
  • Depth reduction of a class of Witten zeta functions,
  • On Mordell-Tornheim sums and multiple zeta values.
• S. A. Zlobin,
  • A certain integral over a triangle,
  • A note on arithmetic properties of multiple zeta values,
  • Integrals over polytopes, multiple zeta values and polylogarithms, and Euler's constant,
  • Generating functions for the values of a multiple zeta function,
  • Special values of generalized polylogarithms,
  • Relations for multiple zeta values.
• H. Żołądek,
  • Note on multiple zeta-values,
  • Linear differential equations and multiple zeta values I. Zeta(2),
  • Linear differential equations and multiple zeta values II. A generalization of the WKB method.
• I. J. Zucker, The evaluation of character Euler double sums.
• W. Zudilin,
  • Algebraic relations for multiple zeta values,
  • One parameter models of Hopf algebras associated with multiple zeta values,
  • Zeta stars,
  • Cyclic q-MZSV sum.

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