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We prove a new linear relation for multiple zeta values. This is a natural generalization of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.

Number Theory · Mathematics 2018-07-04 Hideki Murahara , Takuya Murakami

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…

Number Theory · Mathematics 2024-04-24 Zhonghua Li , Zhenlu Wang

Multiple zeta values (MZVs) are real numbers which are defined by certain multiple series. Recently, many people have researched for relations among them and many relations are well known. In this paper, we get a new relation among them…

Number Theory · Mathematics 2015-12-29 Shin-ya Kadota

We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…

Number Theory · Mathematics 2024-03-01 Takumi Maesaka , Shin-ichiro Seki , Taiki Watanabe

For positive integers $i_1,...,i_k$ with $i_1 > 1$, we define the multiple $t$-value $t(i_1,...,i_k)$ as the sum of those terms in the usual infinite series for the multiple zeta value $\zeta(i_1,...,i_k)$ with odd denominators. Like the…

Number Theory · Mathematics 2020-10-14 Michael E. Hoffman

We present several conjectures on multiple q-zeta values and on the role they play in certain problems of enumerative geometry.

Algebraic Geometry · Mathematics 2014-04-16 Andrei Okounkov

We present a concise method for deriving an explicit formula for $p$-adic multiple zeta values. The formula features a variant of multiple harmonic sums, termed binomial multiple harmonic sums.

Number Theory · Mathematics 2025-12-01 Hidekazu Furusho , David Jarossay

We construct an analytic approach to evaluate odd Euler sums, multiple zeta value $\zeta(3,2,\ldots,2)$ and multiple $t$-value $t\left(3,2,\ldots,2\right)$. Moreover, we also conjecture a closed expression for multiple $t$-value…

Number Theory · Mathematics 2021-11-16 Sarth Chavan , Masato Kobayashi , Jorge Layja

We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when…

Number Theory · Mathematics 2021-02-09 Tanay Wakhare , Christophe Vignat

Bowman and Bradley proved an explicit formula for the sum of multiple zeta values whose indices are the sequence (3,1,3,1,...,3,1) with a number of 2's inserted. Kondo, Saito and Tanaka considered the similar sum of multiple zeta-star…

Number Theory · Mathematics 2012-03-07 Shuji Yamamoto

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

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

In this paper we discuss three types of the mean values of the Euler double zeta function. In order to get results we introduce three approximate formulas for this function.

Number Theory · Mathematics 2013-07-09 Soichi Ikeda , Kaneaki Matsuoka , Yoshikazu Nagata

We prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…

Number Theory · Mathematics 2014-05-27 Shuji Yamamoto

The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manner using an identity that involves the Schur multiple zeta…

Number Theory · Mathematics 2020-11-10 Minoru Hirose , Hideki Murahara , Shingo Saito

Two classes of relations for multiple zeta values are handled algebraically. A restricted sum formula is proved by Eie, Liaw and Ong. The derivation relation is proved by Ihara, Kaneko and Zagier. In this paper we show the latter implies…

Number Theory · Mathematics 2013-03-05 Tatsushi Tanaka

The Ohno relation is a well-known relation among multiple zeta values. Hirose, Onozuka, Sato, and the author investigated the sum related to the Ohno relation and presented two types of new relations and five conjectural formulas. This…

Number Theory · Mathematics 2021-07-27 Hideki Murahara

We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by…

Number Theory · Mathematics 2009-02-17 Tatsushi Tanaka , Noriko Wakabayashi

We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…

Number Theory · Mathematics 2012-10-31 Tomoya Machide

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