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Related papers: A note on Ohno sums for multiple zeta values

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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 Newton series which interpolate finite multiple harmonic sums are useful in the study of multiple zeta values (MZV's). In this paper, we prove that these Newton series can be written as multiple series. As an application, we give a…

Number Theory · Mathematics 2009-05-05 Gaku Kawashima

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

For $k\leq n$, let $E(mn,k)$ be the sum of all multiple zeta values of depth $k$ and weight $mn$ with arguments are multiples of $m\geq 2$. More precisely, $E(mn,k)=\sum_{|\boldsymbol{\alpha}|=n}\zeta(m\alpha_1,m\alpha_2,\ldots,…

Number Theory · Mathematics 2016-08-05 Kwang-Wu Chen , Chan-Liang Chung , Minking Eie

Multiple zeta values are real numbers defined by an infinite series generalizing values of the Riemann zeta function at positive integers. Finite truncations of this series are called multiple harmonic sums and are known to have interesting…

Number Theory · Mathematics 2015-06-12 Julian Rosen

The multiple T-value, which is a variant of multiple zeta value of level two, is introduced by Kaneko and Tsumura. We show that the generating function of a weighted sum of the multiple T-values of fixed weight and depth is given in terms…

Number Theory · Mathematics 2020-12-22 Yoshihiro Takeyama

We find and prove relationships between Riemann zeta values and central binomial sums. We also investigate alternating binomial sums (also called Ap\'ery sums). The study of non-alternating sums leads to an investigation of different types…

High Energy Physics - Theory · Physics 2007-05-23 J. M. Borwein , D. J. Broadhurst , J. Kamnitzer

Hirose, Murahara, and Saito proved that some $t$-adic symmetric multiple zeta values, for indices in which $1$ and $3$ appear alternately in succession, can be expressed as polynomials in Riemann zeta values, and conjectured similar…

Number Theory · Mathematics 2025-03-21 Kento Fujita

Inspired by a 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. Our main result will…

Number Theory · Mathematics 2017-05-16 Henrik Bachmann

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

Let s_1,...,s_d be d positive integers and consider the multiple Hurwitz-zeta value zeta(s_1,...,s_d;-1/2,...,-1/2)/2^w where w=s_1+...+s_d is called the weight. For d<n+1, let T(2n,d) be the sum of all these values with even arguments…

Number Theory · Mathematics 2018-04-06 Jianqiang Zhao

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 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

Kaneko and Yamamoto introduced a convoluted variant of multiple zeta values (MVZs) around 2016. In this paper, we will first establish some explicit formulas involving these values and their alternating version by using iterated integrals,…

Number Theory · Mathematics 2025-08-06 Ce Xu , Jianqiang Zhao

We explore the theory of multiple zeta values (MZVs) and some of their $q$-generalisations. Multiple zeta values are numerical quantities that satisfy several combinatorial relations over the rationals. These relations include two…

Number Theory · Mathematics 2020-07-20 Abel Vleeshouwers

In this paper, we establish some new identities of integrals involving multiple polylogarithm functions and their level two analogues in terms of Hurwitz-type multiple zeta (star) values. Using these identities, we provide new proofs of the…

Number Theory · Mathematics 2025-01-22 Masanobu Kaneko , Weiping Wang , Ce Xu , Jianqiang Zhao

Kawashima's relation is conjecturally one of the largest classes of relations among multiple zeta values. Gaku Kawashima introduced and studied a certain Newton series, which we call the Kawashima function, and deduced his relation by…

Number Theory · Mathematics 2020-12-01 Masanobu Kaneko , Ce Xu , Shuji Yamamoto

We study a general type of series and relate special cases of it to Stirling series, infinite series discussed by Choi and Hoffman, and also to special values of the Arakawa-Kaneko zeta function, complementing and generalizing earlier…

Number Theory · Mathematics 2018-07-03 Markus Kuba , Alois Panholzer

Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of…

Number Theory · Mathematics 2017-10-12 Zhonghua Li , Noriko Wakabayashi

We give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.

Number Theory · Mathematics 2024-10-03 Minoru Hirose
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