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In this paper we present many new families of identities for multiple harmonic sums using binomial coefficients. Some of these generalize a few recent results of Hessami Pilehrood et al. As applications we prove several conjectures…

Number Theory · Mathematics 2018-04-06 Jianqiang Zhao

T. Ito defined an analog of the Arakawa-Kaneko zeta function to obtain relations among Mordell-Tornheim multiple zeta values. In this paper, we develop two things related to an analog of the Arakawa-Kaneko zeta function. One is to find an…

Number Theory · Mathematics 2018-04-02 Ryota Umezawa

We prove three theorems on finite real multiple zeta values: the symmetric formula, the sum formula and the height-one duality theorem. These are analogues of their counterparts on finite multiple zeta values.

Number Theory · Mathematics 2016-01-05 Hideki Murahara

We obtain a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of…

Number Theory · Mathematics 2018-11-02 Zhonghua Li , Chen Qin

In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…

Number Theory · Mathematics 2017-09-04 Chan-Liang Chung , Minking Eie

In this paper, we present some identities for multiple zeta-star values with indices obtained by inserting 3 or 1 into the string 2,...,2. Our identities give analogues of Zagier's evaluation of \zeta(2,...,2,3,2,..., 2) and examples of a…

Number Theory · Mathematics 2014-06-06 Koji Tasaka , Shuji Yamamoto

Recently, the present authors jointly with Tauraso found a family of binomial identities for multiple harmonic sums (MHS) on strings $(\{2\}^a,c,\{2\}^b)$ that appeared to be useful for proving new congruences for MHS as well as new…

Number Theory · Mathematics 2018-06-26 Khodabakhsh Hessami Pilehrood , Tatiana Hessami Pilehrood

We prove a sum formula with 4 parameters among finite alternating multiple zeta values which can be regarded as an alternating version of the result of Kamano on finite multiple zeta values.

Number Theory · Mathematics 2022-02-22 Takumi Anzawa

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

In this paper, we consider infinite-length versions of multiple zeta-star values. We give several explicit formulas for the infinite-length versions of multiple zeta-star values. We also discuss the analytic properties of the map from…

Number Theory · Mathematics 2023-11-01 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

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

The Kaneko-Zagier conjecture states that finite and symmetric multiple zeta values satisfy the same relations. In the previous work with H.~Bachmann and Y.~Takeyama, we proved that the finite and symmetric multiple zeta value are obtained…

Number Theory · Mathematics 2021-03-18 Koji Tasaka

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 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

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

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 set of multiple zeta-star values is a countable dense subset of the half line $(1,+\infty)$. In this paper, we establish some classical Diophantine type results for the set of multiple zeta-star values. Firstly, we give a criterion to…

Number Theory · Mathematics 2025-06-23 Jiangtao Li

In this paper, we formally introduce the notion of Ap{\'e}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in…

Number Theory · Mathematics 2019-12-12 P. Akhilesh

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

The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…

Number Theory · Mathematics 2011-03-11 Shingo Saito , Tatsushi Tanaka , Noriko Wakabayashi