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Related papers: Ohno-type relation for finite multiple zeta values

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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 prove a new linear relation for multiple zeta values. This is a natural generalization of the restricted sum formula proved by Eie, Liaw and Ong. We also present an analogous result for finite multiple zeta values.

Number Theory · Mathematics 2018-07-04 Hideki Murahara , Takuya Murakami

The Kaneko--Zagier conjecture describes a correspondence between finite multiple zeta values and symmetric multiple zeta values. Its refined version has been established by Jarossay, Rosen and Ono--Seki--Yamamoto. In this paper, we…

Number Theory · Mathematics 2022-02-21 Yoshihiro Takeyama , Koji Tasaka

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 prove a sum formula with 4 parameters among finite alternating multiple zeta values which can be regarded as an alternating version of the result of Kamano on finite multiple zeta values.

Number Theory · Mathematics 2022-02-22 Takumi Anzawa

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

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

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

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

Ohno's relation is a well-known relation on the field of the multiple zeta values and has an interpolation to complex function. In this paper, we call its complex function Ohno function and study it. We consider the region of absolute…

Number Theory · Mathematics 2020-12-15 Ken Kamano , Tomokazu Onozuka

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

The sum formula for finite and symmetric multiple zeta values, established by Wakabayashi and the authors, implies that if the weight and depth are fixed and the specified component is required to be more than one, then the values sum up to…

Number Theory · Mathematics 2019-12-25 Hideki Murahara , Shingo Saito

The relationship between the Ohno relation and multiple polylogarithms are discussed. Using this relationship, the algebraic reduction of the Ohno relation is given.

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

One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta functions are a generalization of the multiple zeta functions of…

Number Theory · Mathematics 2025-06-30 Maki Nakasuji , Yasuo Ohno , Wataru Takeda

We study special values of finite multiple harmonic q-series at roots of unity. These objects were recently introduced by the authors and it was shown that they have connections to finite and symmetric multiple zeta values and the…

Number Theory · Mathematics 2018-07-03 Henrik Bachmann , Yoshihiro Takeyama , Koji Tasaka

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 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

The Kaneko-Zagier conjecture states that finite and symmetric multiple zeta values satisfy the same relations. In the previous work with H.~Bachmann and Y.~Takeyama, we proved that the finite and symmetric multiple zeta value are obtained…

Number Theory · Mathematics 2021-03-18 Koji Tasaka

The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case,…

Number Theory · Mathematics 2010-03-18 Li Guo , Bingyong Xie

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