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The cyclic relation obtained in a study by Hirose, Murakami, and the first-named author, is a wide class of relations, which includes the well-known cyclic sum formula for multiple zeta and zeta-star values, and the derivation relation for…

Number Theory · Mathematics 2022-03-17 Hideki Murahara , Tomokazu Onozuka

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

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

In this paper, we formally introduce the notion of Ap{\'e}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in…

Number Theory · Mathematics 2019-12-12 P. Akhilesh

Ohno's relation is a generalization of both the sum formula and the duality formula for multiple zeta values. Oyama gave a similar relation for finite multiple zeta values, defined by Kaneko and Zagier. In this paper, we prove relations of…

Number Theory · Mathematics 2020-06-26 Minoru Hirose , Kohtaro Imatomi , Hideki Murahara , Shingo Saito

Hirose, Saito, and the author established the weighted sum formula for finite multiple zeta(-star) values. In this paper, we present its alternative proof. The proof is also valid for symmetric multiple zeta(-star) values.

Number Theory · Mathematics 2019-07-02 Hideki Murahara

We prove three theorems on finite real multiple zeta values: the symmetric formula, the sum formula and the height-one duality theorem. These are analogues of their counterparts on finite multiple zeta values.

Number Theory · Mathematics 2016-01-05 Hideki Murahara

Ohno-Wakabayashi's cyclic sum formula for multiple zeta-star values is generalized by Igarashi with one or two parameters. In this article, we give a possible answer for one of his problems about a generalization with three parameters.

Number Theory · Mathematics 2024-12-06 Hanamichi Kawamura , Anju Yokoi

Many $\mathbb{Q}$-linear relations exist between multiple zeta values, the most interesting of which are various weighted sum formulas. In this paper, we generalized these to Euler sums and some other variants of multiple zeta values by…

Number Theory · Mathematics 2024-10-04 Sasha Berger , Aarav Chandra , Jasper Jain , Daniel Xu , Ce Xu , J. Zhao

In this paper, we give the values of a certain kind of $q$-multiple zeta functions at roots of unity. Various multiple zeta values have been proposed and studied by many researchers, but these multiple zeta values naturally arise from…

Number Theory · Mathematics 2025-05-15 Takao Komatsu

The sum formula for multiple zeta values are derived, via the Mellin transform, from the Euler connection formula and the Landen connection formula for polylogarithms. These connection formulas for multiple polylogarithms will be considered…

Number Theory · Mathematics 2007-05-23 Jun-ichi Okuda , Kimio Ueno

Recently, a new kind of multiple zeta value level two $T({\bf k})$ (which is called multiple $T$-values) was introduced and studied by Kaneko and Tsumura. In this paper, we define a kind of alternating version of multiple $T$-values, and…

Number Theory · Mathematics 2020-06-23 Ce Xu

We prove and conjecture several relations between multizeta values for $\mathbb{F}_q[t]$, focusing on zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular,…

Number Theory · Mathematics 2013-12-18 José Alejandro Lara Rodríguez , Dinesh S. Thakur

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…

Number Theory · Mathematics 2024-04-24 Zhonghua Li , Zhenlu Wang

The derivation relations for multiple zeta values is proved by Ihara, Kaneko and Zagier. We prove its counterpart for finite multiple zeta values.

Number Theory · Mathematics 2016-02-29 Hideki Murahara

In this paper we prove a weighted sum formula for multiple harmonic sums modulo primes, thereby proving a weighted sum formula for finite multiple zeta values. Our proof utilizes difference equations for the generating series of multiple…

Number Theory · Mathematics 2018-08-03 Minoru Hirose , Hideki Murahara , Shingo Saito

We investigate relations between elliptic multiple zeta values and describe a method to derive the number of indecomposable elements of given weight and length. Our method is based on representing elliptic multiple zeta values as iterated…

High Energy Physics - Theory · Physics 2016-04-26 Johannes Broedel , Nils Matthes , Oliver Schlotterer

In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.

Number Theory · Mathematics 2018-04-06 Haiping Yuan , Jianqiang Zhao

The multiple zeta values (MZVs) have been studied extensively in recent years. Currently there exist a few different types of $q$-analogs of the MZVs ($q$-MZVs) defined and studied by mathematicians and physicists. In this paper, we give a…

Number Theory · Mathematics 2020-05-26 Jianqiang Zhao

We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by…

Number Theory · Mathematics 2009-02-17 Tatsushi Tanaka , Noriko Wakabayashi