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Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…

Number Theory · Mathematics 2015-10-15 Li Guo , Peng Lei , Jianqiang Zhao

We show how infinite series of a certain type involving generalized harmonic numbers can be computed using a knowledge of symmetric functions and multiple zeta values. In particular, we prove and generalize some identities recently…

Number Theory · Mathematics 2017-01-17 Michael E. Hoffman

In this paper, we study specific families of multiple zeta values which closely relate to the linear part of Kawashima's relation. We obtain an explicit basis of these families, and investigate their interpolations to complex functions. As…

Number Theory · Mathematics 2019-10-15 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are…

Number Theory · Mathematics 2018-07-25 Roberto B. Corcino , Hassan Jolany , Cristina B. Corcino , Takao Komatsu

The derivation relations for multiple zeta values is proved by Ihara, Kaneko and Zagier. We prove its counterpart for finite multiple zeta values.

Number Theory · Mathematics 2016-02-29 Hideki Murahara

Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…

Number Theory · Mathematics 2019-04-23 Zhonghua Li

We introduce a $q$-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple $q$-zeta values satisfy a $q$-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the…

Quantum Algebra · Mathematics 2007-06-13 David M. Bradley

Multiple zeta values arise as special values of polylogarithms defined on Riemann surfaces of various genera. Building on the vast knowledge for classical and elliptic multiple zeta values, we explore a canonical extension of the formalism…

High Energy Physics - Theory · Physics 2025-07-30 Konstantin Baune , Johannes Broedel , Egor Im , Zhexian Ji , Yannis Moeckli

We describe in this work all solutions to the problem of renormalizing multiple zeta values at arguments of any sign in a quasi-shuffle compatible way. As a corollary we clarify the relation between different renormalizations at…

Number Theory · Mathematics 2015-11-02 Kurusch Ebrahimi-Fard , Dominique Manchon , Johannes Singer , Jianqiang Zhao

The cyclic sum formulas for multiple zeta and zeta-star values were respectively proved by Hoffman and Ohno, and Ohno and Wakabayashi. Kawasaki and Oyama obtained an analogous formulas for finite multiple zeta and zeta-star values. In this…

Number Theory · Mathematics 2020-09-30 Hideki Murahara

By using the method of iterated integral representations of series, we establish some explicit relationships between multiple zeta values and Integrals of logarithmic functions. As applications of these relations, we show that multiple zeta…

Number Theory · Mathematics 2017-01-03 Ce Xu

We introduce finite and symmetric Mordell-Tornheim type of multiple zeta values and give a new approach to the Kaneko-Zagier conjecture stating that the finite and symmetric multiple zeta values satisfy the same relations.

Number Theory · Mathematics 2020-01-30 Henrik Bachmann , Yoshihiro Takeyama , Koji Tasaka

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…

Number Theory · Mathematics 2023-09-18 Koji Tasaka

In this work we discuss a parameter $\sigma$ on weighted $k$-element multisets of $[n]= \{1,\dots ,n\}$. The sums of weighted $k$-multisets are related to $k$-subsets, $k$-multisets, as well as special instances of truncated interpolated…

Combinatorics · Mathematics 2022-03-02 Markus Kuba

In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on…

Number Theory · Mathematics 2024-02-22 Minoru Hirose

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

Number Theory · Mathematics 2020-08-25 Hideki Murahara , Masataka Ono

We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision…

Number Theory · Mathematics 2014-06-10 Li Guo , Sylvie Paycha , Bin Zhang

We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a…

Number Theory · Mathematics 2019-06-04 Yoshihiro Takeyama

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 between multiple zeta values and multiple zeta…

Number Theory · Mathematics 2017-04-11 Ce Xu

In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula…

Number Theory · Mathematics 2021-05-27 P. Akhilesh