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Ohno-Wakabayashi's cyclic sum formula for multiple zeta-star values is generalized by Igarashi with one or two parameters. In this article, we give a possible answer for one of his problems about a generalization with three parameters.

Number Theory · Mathematics 2024-12-06 Hanamichi Kawamura , Anju Yokoi

Extended double shuffle relations for multiple zeta values are obtained by the fact that any product of regularized multiple zeta values has two different representations, and the case of two-fold product is considered in general. In this…

Number Theory · Mathematics 2019-07-24 Tomoya Machide

In this paper we consider iterated integrals of multiple polylogarithm functions and prove some explicit relations of multiple polylogarithm functions. Then we apply the relations obtained to find numerous formulas of alternating multiple…

Number Theory · Mathematics 2019-08-09 Ce Xu

In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.

Number Theory · Mathematics 2018-04-06 Haiping Yuan , Jianqiang Zhao

The duality relation is a basic family of linear relations for multiple zeta values. The extended double shuffle relation (EDSR) is one of the families of relations expected to generate all linear relations among multiple zeta values, but…

Number Theory · Mathematics 2022-08-19 Aiki Kimura

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

We study relations between the multizeta values for function fields introduced by D. Thakur. The product \zeta(a)\zeta(b) is a linear combination of multizeta values. For q=2, a full conjectural description of how the product of two zeta…

Number Theory · Mathematics 2011-08-25 José Alejandro Lara Rodríguez

We prove a new linear relation for a q-analogue of multiple zeta values. It is a q-extension of the restricted sum formula obtained by Eie, Liaw and Ong for multiple zeta values.

Number Theory · Mathematics 2011-12-02 Yoshihiro Takeyama

We focus on multizeta values of depth two for $\mathbb{F}_q[t]$, where the ratio with another multizeta value of depth two is rational. In characteristic 2, we prove some extra relations between multizeta values of depth 2 and the same…

Number Theory · Mathematics 2022-08-15 José Alejandro Lara Rodríguez

The Ohno relation is one of the most celebrated results in the theory of multiple zeta values, which are iterated integrals from $0$ to $1$. In a previous paper, the authors generalized the Ohno relation to regularized multiple zeta values,…

Number Theory · Mathematics 2024-11-26 Minoru Hirose , Hideki Murahara , Shingo Saito

We introduce and study a ``level two'' analogue of finite multiple zeta values. We give conjectural bases of the space of finite Euler sums as well as that of usual finite multiple zeta values in terms of these newly defined elements. A…

Number Theory · Mathematics 2021-09-28 Masanobu Kaneko , Takuya Murakami , Amane Yoshihara

The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case,…

Number Theory · Mathematics 2010-03-18 Li Guo , Bingyong Xie

We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double $T$-values, and some double $L$-values. Also presented is a…

Number Theory · Mathematics 2024-10-01 Masanobu Kaneko , Hirofumi Tsumura

An explicit formula for the height-one multiple zeta values was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values.

Number Theory · Mathematics 2017-11-15 Hideki Murahara , Mika Sakata

In this paper we prove some new identities for multiple zeta values and multiple zeta star values of arbitrary depth by using the methods of integral computations of logarithm function and iterated integral representations of series. By…

Number Theory · Mathematics 2017-10-20 Ce Xu

We study multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota--Baxter algebras.

Number Theory · Mathematics 2014-10-14 Kurusch Ebrahimi-Fard , Li Guo

We present a unified approach which gives completely elementary proofs of three weighted sum formulae for double zeta values. This approach also leads to new evaluations of sums relating to the harmonic numbers, the alternating double zeta…

Number Theory · Mathematics 2012-06-13 James Wan

We define two finite q-analogs of certain multiple harmonic series with an arbitrary number of free parameters, and prove identities for these q-analogs, expressing them in terms of multiply nested sums involving the Gaussian binomial…

Combinatorics · Mathematics 2007-06-13 David M. Bradley

We study the Hurwitz-type analogue of Schur multiple zeta-functions involving shifting parameters. We extend various formulas, known for ordinary Schur multiple zeta-functions, to the case of Hurwitz type. We also mention unpublished…

Number Theory · Mathematics 2025-03-27 Kohji Matsumoto , Maki Nakasuji

We prove some relations for the $q$-multiple zeta values ($q$MZV). They are $q$-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier relation for the multiple zeta values (MZV). We discuss the problem to determine the…

Quantum Algebra · Mathematics 2007-05-23 Jun-ichi Okuda , Yoshihiro Takeyama