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Journal of number theory, ISSN 0022-314X, 2017, Volume 171, pp. 227 - 251
We study an elliptic analogue of multiple zeta values, the elliptic multiple zeta values of Enriquez, which are the coefficients of the elliptic KZB associator... 
Eisenstein series | Elliptic multiple zeta values | Elliptic polylogarithms | Elliptic associators | Iterated integrals | Theta functions | MATHEMATICS | Algebra
Journal Article
Advances in Mathematics, ISSN 0001-8708, 07/2018, Volume 333, pp. 570 - 619
We introduce Schur multiple zeta functions which interpolate both the multiple zeta and multiple zeta-star functions of the Euler... 
Schur functions | Multiple zeta functions | Quasi-symmetric functions | Jacobi–Trudi formula | MATHEMATICS | Jacobi-Trudi formula | STAR VALUES
Journal Article
Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2014, Volume 47, Issue 15, pp. 155401 - 15
We revisit the tree-level closed superstring amplitude and identify its alpha'=expansion as series with single-valued multiple zeta values as coefficients... 
stringtheory | amplitudes | multiple zeta values | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | String theory | Gravitation | Amplitudes | Unity | Mathematical analysis | Lie groups | Representations | Gamma function | Joints
Journal Article
Journal of Algebra, ISSN 0021-8693, 02/2020, Volume 543, pp. 111 - 155
•A rigorous construction of Arborified Zeta Values (AZVs) as iterated series and integrals and a proof of their convergence... 
Multiple zeta values | Rooted trees | Shuffle products | Rota-Baxter algebras | MATHEMATICS
Journal Article
by Xu, Ce
Journal of number theory, ISSN 0022-314X, 2017, Volume 177, pp. 443 - 478
In this paper, we establish some expressions of series involving harmonic numbers and Stirling numbers of the first kind in terms of multiple zeta values, and present some new relationships... 
Multiple star harmonic number | Euler sum | Multiple zeta star value | Multiple zeta value | Multiple harmonic number | INTEGRALS | MATHEMATICS | SERIES | NUMBERS | DUALITY | FORMULAS | RIEMANN ZETA | Mathematics - Number Theory
Journal Article
Ramanujan Journal, ISSN 1382-4090, 2019, Volume 49, Issue 1, pp. 215 - 230
Journal Article
Journal of the Australian Mathematical Society (2001), ISSN 1446-7887, 06/2018, Volume 104, Issue 3, pp. 289 - 307
Inspired by the recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki, we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values... 
Schur functions | interpolated multiple zeta values | multiple zeta values | Jacobi-Trudi formula | MATHEMATICS | STAR VALUES
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2018, Volume 290, Issue 3, pp. 1173 - 1197
We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star... 
Hypergeometric functions | 11M41 | Jacobi–Trudi formula | Hankel determinants | Multiple zeta values | Schur functions | 05E05 | Mathematics, general | Mathematics | 33C05 | MATHEMATICS | Jacobi-Trudi formula
Journal Article
COMPOSITIO MATHEMATICA, ISSN 0010-437X, 12/2018, Volume 154, Issue 12, pp. 2701 - 2721
We study the values of finite multiple harmonic q-series at a primitive root of unity and show that these specialize to the finite multiple zeta value (FMZV... 
MATHEMATICS | finite multiple harmonic q-series | symmetric multiple zeta (star) values | finite multiple zeta (star) values | Kaneko-Zagier conjecture | multiple zeta (star) values | SUM FORMULA | Mathematics - Number Theory
Journal Article
Advances in mathematics (New York. 1965), ISSN 0001-8708, 2016, Volume 298, pp. 254 - 285
Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a q-analog of multiple zeta values possessing... 
Rota–Baxter algebra | Double shuffle relations | Hoffman–Ohno relation | Infinitesimal bialgebra | q-Analogues | Derivation relations | Multiple zeta values | Duality | Hopf algebra | Hoffman-Ohno relation | Rota-Baxter algebra | Q-Analogues | MATHEMATICS | Algebra | Singers | Mathematics - Number Theory
Journal Article
Journal of Algebra, ISSN 0021-8693, 07/2013, Volume 385, pp. 102 - 114
We define polynomials of one variable t whose values at t=0and1 are the multiple zeta values and the multiple zeta-star values, respectively... 
Multiple zeta values | Two-one conjecture | Multiple zeta-star values | Cyclic sum formula | Sum formula | MATHEMATICS
Journal Article
Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2016, Volume 49, Issue 15, p. 155203
We investigate relations between elliptic multiple zeta values (eMZVs) and describe a method to derive the number of indecomposable elements of given weight and length... 
string-theory one-loop amplitude | iterated integrals | derivation algebra | elliptic multiple zeta value | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL
Journal Article
Journal of symbolic computation, ISSN 0747-7171, 11/2020, Volume 101, pp. 109 - 127
Flajolet and Salvy pointed out that every Euler sum is a Q-linear combination of multiple zeta values... 
Euler sums | Multiple zeta values | Permutations | Compositions | Harmonic numbers
Journal Article
Journal of physics. A, Mathematical and theoretical, ISSN 1751-8121, 2018, Volume 51, Issue 28, p. 285401
We consider a generalization of elliptic multiple zeta values, which we call twisted elliptic multiple zeta values... 
string theory | cyclotomic multiple zeta values | elliptic multiple zeta values | open-string one-loop amplitude | PHYSICS, MULTIDISCIPLINARY | UNITY | SUPERSTRING THEORY | POLYLOGARITHM VALUES | PHYSICS, MATHEMATICAL | LA POLYAKOV | INTEGRALS | FORMS | ALGEBRAS | ASSOCIATORS | ROOTS
Journal Article
Journal of Algebra, ISSN 0021-8693, 2011, Volume 332, Issue 1, pp. 187 - 208
We discuss an algebraic connection between two kinds of multiple zeta values or their q-analogues: the ( q... 
Multiple zeta values | Multiple zeta-star values | Harmonic algebra | q-Series | Q-Series | POLYLOGARITHMS | MATHEMATICS | HARMONIC SERIES | ALGEBRA | SUM
Journal Article
Ramanujan Journal, ISSN 1382-4090, 06/2010, Volume 22, Issue 2, pp. 153 - 162
.... By rewriting Ohno's sum formula, we are able to deduce a new class of relations between Euler sums and the values of zeta. 
Euler sums | Multiple zeta-star values | Zeta values | Poly-Bernoulli numbers | MATHEMATICS | VALUES
Journal Article
Journal of algebra, ISSN 0021-8693, 2008, Volume 319, Issue 9, pp. 3770 - 3809
Journal Article
Taiwanese Journal of Mathematics, ISSN 1027-5487, 6/2018, Volume 22, Issue 3, pp. 529 - 543
Using the combinatorial descriptions of stuffle product, we obtain recursive formulas for the stuffle product of multiple zeta values and of multiple zeta-star values... 
Multiple zeta values | Stuffle product | Multiple zeta-star values | MATHEMATICS | DECOMPOSITION | multiple zeta-star values | Stuffel product | multiple zeta values | SHUFFLE PRODUCT
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 04/2017, Volume 13, Issue 3, pp. 705 - 716
For k ≤ n , let E ( 2 n , k ) be the sum of all multiple zeta values with even arguments whose weight is 2 n and whose depth is k . Of course E ( 2 n , 1 ) is the value ζ ( 2 n... 
Multiple zeta values | multiple zeta-star values | symmetric functions | Bernoulli numbers | MATHEMATICS | GENERATING FUNCTION | HARMONIC SERIES | Mathematics - Number Theory
Journal Article
Integral transforms and special functions, ISSN 1476-8291, 2018, Volume 30, Issue 4, pp. 282 - 300
.... Since , we call this function as a generalized Arakawa-Kaneko zeta function. In this paper, we investigate the properties and values of with different values s, x, and p... 
generalized harmonic functions | Arakawa-Kaneko zeta functions | multiple zeta values | modified Bell polynomials | MATHEMATICS | MATHEMATICS, APPLIED | VALUES | POLY-BERNOULLI NUMBERS | Integers | Real numbers | Numbers
Journal Article
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