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In this paper, we construct generating functions of alternating sums for the Arakawa-Kaneko zeta values. From the expressions, we show alternating sum formulas for them. Based on these results, we apply the same method to other zeta values.

Number Theory · Mathematics 2024-03-25 Yuta Nishimura

We prove the cyclic sum formulas for certain two-parameter multiple series. These are new and non-trivial generalizations of the cyclic sum formulas for multiple zeta values and multiple zeta-star values.

Number Theory · Mathematics 2022-06-03 Masahiro Igarashi

The objective of the paper is the study of Mneimneh-like sums with a parametric variant of the multiple harmonic-star values. We generalize and resolve the Pan-Xu conjecture on generalized Mneimneh-like sums and present their…

Number Theory · Mathematics 2024-08-30 Marian Genčev

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

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of…

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

The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.

Number Theory · Mathematics 2026-03-03 Anju Yokoi

We study the algebra MD of generating function for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in Q arising from the…

Number Theory · Mathematics 2014-07-28 Henrik Bachmann , Ulf Kuehn

In this paper, we investigate the sums of mutliple zeta(-star) values of height one: $Z_{\pm}(n)=\sum_{a+b=n} (\pm 1)^b\zeta(\{1\}^a,b+2)$, $Z_{\pm}^{\star}(n)=\sum_{a+b=n} (\pm 1)^b\zeta^{\star}(\{1\}^a,b+2)$. In particular, we prove that…

Number Theory · Mathematics 2021-10-04 Kwang-Wu Chen , Minking Eie

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 prove some weighted sum formulas for half multiple zeta values, half finite multiple zeta values, and half symmetric multiple zeta values. The key point of our proof is Dougall's identity for the generalized hypergeometric function…

Number Theory · Mathematics 2023-04-07 Hanamichi Kawamura , Takumi Maesaka , Masataka Ono

One of the generalizations of multiple zeta values is the $q$-version, and in the case of finite sums, they may be expressed explicitly in polynomial form. Several results have been found when the powers of the factors in the denominator…

Number Theory · Mathematics 2025-12-09 Yuri Bilu , Hideaki Ishikawa , Takao Komatsu

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 provide a framework for relating certain q-series defined by sums over partitions to multiple zeta values. In particular, we introduce a space of polynomial functions on partitions for which the associated q-series are q-analogues of…

Number Theory · Mathematics 2023-08-22 Henrik Bachmann , Jan-Willem van Ittersum

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

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 article, we study the multiple zeta functions (MZF) and some of its variants at identical arguments. Using the harmonic product, these functions can be expressed as polynomials in the Riemann zeta function. Firstly, we note that an…

Number Theory · Mathematics 2026-03-31 Pawan Singh Mehta

In this paper, we study the weighted sums of multiple t-values and of multiple t-star values at even arguments. Some general weighted sum formulas are given, where the weight coefficients are given by (symmetric) polynomials of the…

Number Theory · Mathematics 2019-08-09 Zhonghua Li , Ce Xu

We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realization of symmetric functions and offers a unified method to…

Combinatorics · Mathematics 2020-08-10 Naihuan Jing , Natasha Rozhkovskaya

In this paper, we study sum formulas for Schur multiple zeta values and give a generalization of the sum formulas for multiple zeta(-star) values. We show that for ribbons of certain types, the sum over all admissible Young tableaux of this…

Number Theory · Mathematics 2023-06-05 Henrik Bachmann , Shin-ya Kadota , Yuta Suzuki , Shuji Yamamoto , Yoshinori Yamasaki

The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite multiple zeta values.

Number Theory · Mathematics 2015-08-11 Shingo Saito , Noriko Wakabayashi