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We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes,…

Number Theory · Mathematics 2017-11-28 Henrik Bachmann , Yoshinori Yamasaki

A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum…

Number Theory · Mathematics 2013-03-12 Tomoya Machide

We give three identities involving multiple zeta values of height one and of maximal height; an explicit formula for the height-one multiple zeta values, a regularized sum formula, and a sum formula for the multiple zeta values of maximal…

Number Theory · Mathematics 2019-02-20 Masanobu Kaneko , Mika Sakata

In this paper, we study the generating functions of multiple $t$-star values with an arbitrary number of blocks of twos, which are based on the results of the corresponding generating functions of multiple $t$-harmonic star sums. These…

Number Theory · Mathematics 2022-12-20 Zhonghua Li , Lu Yan

In this paper, we work out some explicit formulae for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. As applications of these formulae, we give new closed form representations of several quadratic…

Number Theory · Mathematics 2017-01-02 Ce Xu , Yingyue Yang , Jianwen Zhang

We introduce finite and symmetric Mordell-Tornheim type of multiple zeta values and give a new approach to the Kaneko-Zagier conjecture stating that the finite and symmetric multiple zeta values satisfy the same relations.

Number Theory · Mathematics 2020-01-30 Henrik Bachmann , Yoshihiro Takeyama , Koji Tasaka

We provide evaluations of several recently studied higher and multiple Mahler measures using log-sine integrals. This is complemented with an analysis of generating functions and identities for log-sine integrals which allows the…

Classical Analysis and ODEs · Mathematics 2011-03-29 Jonathan M. Borwein , Armin Straub

Multiples zeta values and alternating multiple zeta values in positive characteristic were introduced by Thakur and Harada as analogues of classical multiple zeta values of Euler and Euler sums. In this paper we determine all linear…

Number Theory · Mathematics 2024-06-11 Bo-Hae Im , Hojin Kim , Khac Nhuan Le , Tuan Ngo Dac , Lan Huong Pham

We show how the formulas in paper Variae considerationes circa series hypergeometricas written by Euler imply the duplication formula for the Gamma-function. This paper can be seen as an Addendum to a previous paper by the author.

History and Overview · Mathematics 2023-07-25 Alexander Aycock

By combining classical techniques together with two novel asymptotic identities contained in [FL], we analyse certain single sums of Riemann-zeta type. In addition, we analyse Euler-Zagier double exponential sums for particular values of…

Classical Analysis and ODEs · Mathematics 2018-11-09 Konstantinos Kalimeris , Athanassios S. Fokas

We give systematic method to evaluate a large class of one-dimensional integral relating to multiple zeta values (MZV) and colored MZV. We also apply the technique of iterated integrals and regularization to elucidate the nature of some…

Number Theory · Mathematics 2024-01-30 Kam Cheong Au

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

In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.

Number Theory · Mathematics 2009-12-31 T. Kim

Classical multiple zeta values can be viewed as iterated integrals of the differentials $\frac{dt}{t}, \frac{dt}{1-t}$ from $0$ to $1$. In this paper, we reprove Brown's theorem: For $a_i, b_i, c_{ij}\in \mathbb{Z}$, the iterated integral…

Number Theory · Mathematics 2023-02-24 Jiangtao Li

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

In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new…

Number Theory · Mathematics 2024-03-29 Ende Pan , Ce Xu

In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…

Number Theory · Mathematics 2017-01-03 Ce Xu

We give a new and very concise proof of the existence of a holomorphic continuation for a large class of twisted multivariable zeta functions. To do this, we use a simple method of "decalage" that avoids using an integral representation of…

Number Theory · Mathematics 2007-05-23 Marc De Crisenoy , Driss Essouabri

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

In this paper, we obtain some formulas for double nonlinear Euler sums involving harmonic numbers and alternating harmonic numbers. By using these formulas, we give new closed form sums of several quadratic Euler series through Riemann zeta…

Number Theory · Mathematics 2017-01-16 Ce Xu