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We prove a new linear relation for a q-analogue of multiple zeta values. It is a q-extension of the restricted sum formula obtained by Eie, Liaw and Ong for multiple zeta values.

Number Theory · Mathematics 2011-12-02 Yoshihiro Takeyama

The cyclic sum formulas for multiple zeta and zeta-star values were respectively proved by Hoffman and Ohno, and Ohno and Wakabayashi. Kawasaki and Oyama obtained an analogous formulas for finite multiple zeta and zeta-star values. In this…

Number Theory · Mathematics 2020-09-30 Hideki Murahara

We introduce an iterated integral version of (generalized) log-sine integrals (iterated log-sine integrals) and prove a relation between a multiple polylogarithm and iterated log-sine integrals. We also give a new method for obtaining…

Number Theory · Mathematics 2019-04-23 Ryota Umezawa

We prove some relations for the $q$-multiple zeta values ($q$MZV). They are $q$-analogues of the cyclic sum formula, the Ohno relation and the Ohno-Zagier relation for the multiple zeta values (MZV). We discuss the problem to determine the…

Quantum Algebra · Mathematics 2007-05-23 Jun-ichi Okuda , Yoshihiro Takeyama

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

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

Number Theory · Mathematics 2020-08-25 Hideki Murahara , Masataka Ono

The sum formula is a well known relation in the field of the multiple zeta values. In this paper, we present its generalization for the Euler-Zagier multiple zeta function.

Number Theory · Mathematics 2021-07-28 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.

Number Theory · Mathematics 2007-05-23 Sergey Zlobin

We give a new proof of the duality of multiple zeta values, which makes no use of the iterated integrals. The same method is also applicable to Ohno's relation for ($q$-)multiple zeta values.

Number Theory · Mathematics 2019-02-05 Shin-ichiro Seki , Shuji Yamamoto

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 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

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

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

Recently, Maesaka, Watanabe, and the third author discovered a phenomenon where the iterated integral expressions of multiple zeta values become discretized. In this paper, we extend their result to the case of multiple polylogarithms and…

Number Theory · Mathematics 2024-04-24 Minoru Hirose , Toshiki Matsusaka , Shin-ichiro Seki

We explore the theory of multiple zeta values (MZVs) and some of their $q$-generalisations. Multiple zeta values are numerical quantities that satisfy several combinatorial relations over the rationals. These relations include two…

Number Theory · Mathematics 2020-07-20 Abel Vleeshouwers

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

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 establish finite analogues of the identities known as the Aoki-Ohno relation and the Le-Murakami relation in the theory of multiple zeta values. We use an explicit form of a generating series given by Aoki and Ohno.

Number Theory · Mathematics 2018-10-12 Masanobu Kaneko , Kojiro Oyama , Shingo Saito

In this paper, we give an elementary account into Zagier's formula for multiple zeta values involving Hoffman elements. Our approach allows us to obtain direct proof in a special case via rational zeta series involving the coefficient…

Number Theory · Mathematics 2020-11-25 Cezar Lupu

We study relations between the multizeta values for function fields introduced by D. Thakur. The product \zeta(a)\zeta(b) is a linear combination of multizeta values. For q=2, a full conjectural description of how the product of two zeta…

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