English
Related papers

Related papers: Derivation relations and duality for the sum of mu…

200 papers

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

We consider the problem of deducing the duality relation from the extended double shuffle relation for multiple zeta values. Especially we prove that the duality relation for double zeta values and that for the sum of multiple zeta values…

Number Theory · Mathematics 2017-03-14 Naho Kawasaki , Tatsushi Tanaka

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

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

Two classes of relations for multiple zeta values are handled algebraically. A restricted sum formula is proved by Eie, Liaw and Ong. The derivation relation is proved by Ihara, Kaneko and Zagier. In this paper we show the latter implies…

Number Theory · Mathematics 2013-03-05 Tatsushi Tanaka

In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…

Number Theory · Mathematics 2017-09-04 Chan-Liang Chung , Minking Eie

In this paper, we study specific families of multiple zeta values which closely relate to the linear part of Kawashima's relation. We obtain an explicit basis of these families, and investigate their interpolations to complex functions. As…

Number Theory · Mathematics 2019-10-15 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

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 the study on multiple zeta values, the duality formula is one of the families of basic relations and plays an important role in the investigation of algebraic structure of the space spanned by all multiple zeta values along with the…

Number Theory · Mathematics 2021-09-30 Maki Nakasuji , Yasuo Ohno

The sum formula is one of the most well-known relations among multiple zeta values. This paper proves a conjecture of Kaneko predicting that an analogous formula holds for finite multiple zeta values.

Number Theory · Mathematics 2015-08-11 Shingo Saito , Noriko Wakabayashi

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

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 show that a duality formula for certain parametrized multiple series yields numerous relations among them. As a result, we obtain a new relation among extended multiple zeta values, which is an extension of Ohno's relation for multiple…

Number Theory · Mathematics 2023-03-28 Masahiro Igarashi

The multiple T-value, which is a variant of multiple zeta value of level two, is introduced by Kaneko and Tsumura. We show that the generating function of a weighted sum of the multiple T-values of fixed weight and depth is given in terms…

Number Theory · Mathematics 2020-12-22 Yoshihiro Takeyama

The Ohno relation is a well-known relation among multiple zeta values. Hirose, Onozuka, Sato, and the author investigated the sum related to the Ohno relation and presented two types of new relations and five conjectural formulas. This…

Number Theory · Mathematics 2021-07-27 Hideki Murahara

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

Ohno's relation is a well-known relation among multiple zeta values.In this paper, we prove Ohno-type relation for finite multiple zeta values, which is conjectured by Kaneko.As a corollary, we give an alternative proof of the sum formula…

Number Theory · Mathematics 2017-09-26 Kojiro Oyama

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

Recently, Masanobu Kaneko introduced a conjecture on an extension of the derivation relation for multiple zeta values. The goal of the present paper is to present a proof of this conjecture by reducing it to a class of relations for…

Number Theory · Mathematics 2008-05-28 Tatsushi Tanaka

The duality relation is a basic family of linear relations for multiple zeta values. The extended double shuffle relation (EDSR) is one of the families of relations expected to generate all linear relations among multiple zeta values, but…

Number Theory · Mathematics 2022-08-19 Aiki Kimura
‹ Prev 1 2 3 10 Next ›