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Related papers: Stuffle product formulas of multiple zeta values

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In this paper, we explain several conjectures about how a product of two Carlitz-Goss zeta values can be expressed as a F_p-linear combination of Thakur's multizeta values, generalizing the q=2 case dealt by D. Thakur in Relations between…

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

In this paper we consider a family of multiple Hurwitz zeta values with bi-indices parameterized by $\mu$ with $\Ree(\mu)>0$. These values are equipped with both the $\mu$-stuffle product from their series definition and the shuffle product…

Number Theory · Mathematics 2024-02-20 Jia Li , Jianqiang Zhao

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

In this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on…

Number Theory · Mathematics 2024-02-22 Minoru Hirose

In this paper, we give some explicit evaluations of multiple zeta-star values which are rational multiple of powers of $\pi^2$.

Number Theory · Mathematics 2007-10-18 Shuichi Muneta

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 exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…

Number Theory · Mathematics 2016-05-19 Robert Schneider

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 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

We derive a product formula for the multiple stochastic integrals with respect to Levy process. The idea is to use exponential vectors and the polarization technique which greatly simplify the argument.

Probability · Mathematics 2020-06-26 Nishant Agrawal , Yaozhong Hu , Neha Sharma

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

We give new closed and explicit formulas for "multiple zeta values" at non-positive integers of generalized Euler-Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions…

Number Theory · Mathematics 2018-12-11 Driss Essouabri , Kohji Matsumoto

We study some infinite products of absolute zeta functions. Especially, we consider the convergence and the rationality of them.

Number Theory · Mathematics 2021-06-18 Nobushige Kurokawa , Hidekazu Tanaka

It is known that the values of multiple zeta functions (MZFs) at non-positive integers can be expressed by Bernoulli numbers. This paper gives explicit formulas for the values of MZFs and multiple zeta star functions (MZSFs) at non-positive…

Number Theory · Mathematics 2025-08-19 Yoni Ishii , Takeshi Shinohara

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

We introduce the balanced multiple q-zeta values. They give a new model for multiple q-zeta values, whose product formula combines the shuffle and stuffle product for multiple zeta values in a natural way. Moreover, the balanced multiple…

Number Theory · Mathematics 2025-09-03 Annika Burmester

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

We show that any convergent (shuffle) arborified zeta value admits a series representation. This justifies the introduction of a new generalisation to rooted forests of multiple zeta values, and we study its algebraic properties. As a…

Number Theory · Mathematics 2023-10-05 Pierre J. Clavier , Dorian Perrot

We combine the powerful method of Wilf-Zeilberger pairs with systematic theory of multiple zeta values to prove a large number of series identities due to Z.W. Sun, many of them have been long standing conjectures.

Number Theory · Mathematics 2024-12-25 Kam Cheong Au

The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.

Number Theory · Mathematics 2011-05-10 Zhong-hua Li