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We study a refinement of the symmetric multiple zeta value, called the $t$-adic symmetric multiple zeta value, by considering its finite truncation. More precisely, two kinds of regularizations (harmonic and shuffle) give two kinds of the…

Number Theory · Mathematics 2021-01-12 Masataka Ono , Shin-ichiro Seki , Shuji Yamamoto

The derivation relation is a well known relation among multiple zeta values, which was first obtained by Ihara, Kaneko and Zagier. The analogous formula for finite multiple zeta values, which we call the derivation relation for finite…

Number Theory · Mathematics 2018-09-25 Yasunobu Horikawa , Hideki Murahara , Kojiro Oyama

Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…

Number Theory · Mathematics 2019-04-23 Zhonghua Li

Let $l\ge 1$ be an integer. For any multiple index $\mathbf{s}=(s_1,s_2,\cdots,s_l)\in\mathbb{Z}_{\geq 1}^l$ with $s_l>1$, the multiple zeta value (MZV for short) is defined by \begin{align*} \zeta(s_1,s_2,\cdots,s_l):=\sum_{1\leq…

Number Theory · Mathematics 2026-03-03 Jinmin Yu , Shaofang Hong

In this paper, we study various twisted A-harmonic sums, named following the seminal log-algebraicity papers of G. Anderson. These objects are partial sums of new types of special zeta values introduced by the first author and linked to…

Number Theory · Mathematics 2016-06-17 Federico Pellarin , Rudolph Perkins

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

There has been an avalanche of recent research on multiple zeta values. We propose dividing identities for multiple zeta values into structural and specific types. Structural identities are valid for any generalized multiple zeta function,…

Number Theory · Mathematics 2021-02-09 T. Wakhare , C. Vignat

In this paper, we show some expressions of certain $q$-multiple zeta-star values at roots of unity. These explicit formulas are expressed by using the determinants or Bell polynomials. Explicit formulas for other types of values can be…

Number Theory · Mathematics 2025-06-23 Takao Komatsu

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…

History and Overview · Mathematics 2008-02-17 Donal F. Connon

In this paper, we employ the theories and techniques of hypergeometric functions to provide two distinct proofs of the conjectured identities involving multiple Ap\'ery-like series with central binomial coefficients and multiple harmonic…

Number Theory · Mathematics 2025-10-13 Ce Xu

It is shown that novel relations between multiple zeta values and single-variable multiple polylogarithms at 1/2 (delta values) can be derived by comparing two distinct, yet a priori equal, series formulae for the Drinfeld associator (from…

Number Theory · Mathematics 2025-04-24 Cameron James Deverall Kemp

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

We study the Ohno-Zagier type relation for multiple $t$-values and multiple $t$-star values. We represent the generating function of sums of multiple $t$-(star) values with fixed weight, depth and height in terms of the generalized…

Number Theory · Mathematics 2022-04-19 Zhonghua Li , Yutong Song

In this note we introduce multi-interpolated multiple zeta values. We provide a basic decomposition of these objects involving ordered partitions. We also obtain identities for special instances of multi-interpolated multiple zeta values…

Combinatorics · Mathematics 2022-02-04 Markus Kuba

This paper pursues positive characteristic analogues of the results of Furusho, Komori, Matsumoto and Tsumura on $p$-adic multiple $L$-functions. We consider $\infty$-adic and $v$-adic multiple zeta functions concerned by Angl\`{e}s, Ngo…

Number Theory · Mathematics 2022-02-01 Daichi Matsuzuki

In this paper we shall consider a few variants of the motivic multiple zeta values of level two by restricting the summation indices in the definition of multiple zeta values to some fixed parity patterns. These include Hoffman's multiple…

Number Theory · Mathematics 2023-10-25 Ce Xu , Jianqiang Zhao

The purpose of this paper is two-fold. First, we consider the classical Mordell--Tornheim zeta values and their alternating version. It is well-known that these values can be expressed as rational linear combinations of multiple zeta values…

Number Theory · Mathematics 2025-08-06 Crystal Wang , Jianqiang Zhao

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

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

By using various expansions of the parametric digamma function and the method of residue computations, we study three variants of the linear Euler sums, related Hoffman's double $t$-values and Kaneko-Tsumura's double $T$-values, and…

Number Theory · Mathematics 2021-08-31 Weiping Wang , Ce Xu