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We state and prove a function field analogue of Furusho for multiple zeta values.

Number Theory · Mathematics 2020-07-09 Chieh-Yu Chang , Yoshinori Mishiba

Ihara, Kaneko, and Zagier proved the derivation relation for multiple zeta values. The first named author obtained its counterpart for finite multiple zeta values in $\mathcal{A}$. In this paper, we present its generalization in…

Number Theory · Mathematics 2019-11-12 Hideki Murahara , Tomokazu Onozuka

Ohno's relation is a well known formula among multiple zeta values. In this paper, we present its interpolation to complex functions.

Number Theory · Mathematics 2018-08-23 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

We prove some generalizations of the sum formula for multiple zeta values by using Hiroyuki Ochiai's method of proving the sum formula.

Number Theory · Mathematics 2022-06-03 Masahiro Igarashi

We review motivic aspects of multiple zeta values, and as an application, we give an exact-numerical algorithm to decompose any (motivic) multiple zeta value of given weight into a chosen basis up to that weight.

Number Theory · Mathematics 2011-02-09 Francis Brown

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

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

The theory of finite automata applies to the study on relations of multiple zeta values.

Number Theory · Mathematics 2007-05-23 Sinya Kitani , Eiki Sawada , Kimio Ueno

Multiple zeta functions of Arakawa-Kaneko and Euler-Zagier types are known as generalizations of the Riemann zeta function. In 2018, Kaneko and Tsumura proved that the multiple zeta functions of Arakawa-Kaneko type can be expressed as a…

Number Theory · Mathematics 2025-07-22 Naho Kawasaki

We give a weighted sum formula for the double polylogarithm in two variables, from which we can recover the classical weighted sum formulas for double zeta values, double $T$-values, and some double $L$-values. Also presented is a…

Number Theory · Mathematics 2024-10-01 Masanobu Kaneko , Hirofumi Tsumura

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

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

A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.

General Mathematics · Mathematics 2010-10-22 Armen Bagdasaryan

We investigate linear relations among a class of iterated integrals on the Riemann sphere minus four points $0,1,z$ and $\infty$. Generalization of the duality formula and the sum formula for multiple zeta values to the iterated integrals…

Number Theory · Mathematics 2017-04-24 Minoru Hirose , Kohei Iwaki , Nobuo Sato , Koji Tasaka

In this paper, we prove that certain parametrized multiple series which generalize multiple zeta values satisfy the same relation as Ohno's relation for multiple zeta values. This is a parametrized generalization of Ohno's relation for…

Number Theory · Mathematics 2011-04-21 Masahiro Igarashi

We evaluate the multiple zeta values $\zeta(\{2\}^k)$ by proving a certain factorization property. The proof uses a combinatorial bijection and elementary telescoping series. We show how the infinite product for the sine function in fact…

Number Theory · Mathematics 2019-11-19 Mario DeFranco

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

The special values of multiple polylogarithms, which including multiple zeta values, appear some fields of mathematics and physics. Many kinds of their linear relations are investigated as well as their algebraic relations. From the…

Classical Analysis and ODEs · Mathematics 2007-05-23 Jun-ichi Okuda

In this paper, we consider infinite-length versions of multiple zeta-star values. We give several explicit formulas for the infinite-length versions of multiple zeta-star values. We also discuss the analytic properties of the map from…

Number Theory · Mathematics 2023-11-01 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

Multiple zeta-star values are variants of multiple zeta values which allow equality in the definition. Similar to the theory of continued fractions, every real number which is greater than $1$ can be realized as an unique infinite multiple…

Number Theory · Mathematics 2026-04-10 Jiangtao Li , Siyu Yang