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Related papers: A note on derivation relations for multiple zeta v…

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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

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…

Number Theory · Mathematics 2023-09-18 Koji Tasaka

We introduce finite and symmetric Mordell-Tornheim type of multiple zeta values and give a new approach to the Kaneko-Zagier conjecture stating that the finite and symmetric multiple zeta values satisfy the same relations.

Number Theory · Mathematics 2020-01-30 Henrik Bachmann , Yoshihiro Takeyama , Koji Tasaka

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

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

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

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 Ohno relation is one of the most celebrated results in the theory of multiple zeta values, which are iterated integrals from $0$ to $1$. In a previous paper, the authors generalized the Ohno relation to regularized multiple zeta values,…

Number Theory · Mathematics 2024-11-26 Minoru Hirose , Hideki Murahara , Shingo Saito

The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined for indices, is invariant under taking duals. In this paper, we generalize the Ohno relation to regularized multiple zeta values by…

Number Theory · Mathematics 2021-05-21 Minoru Hirose , Hideki Murahara , Shingo Saito

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

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

This paper focuses linear and algebraic relations among multiple zeta values which were obtained in knot theory. It is shown that they can be derived from the associator relations, i.e. the pentagon equation and the shuffle relation.

Quantum Algebra · Mathematics 2020-05-05 Hidekazu Furusho

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

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

We introduce derivations on the algebra of multiple harmonic q-series and show that they generate linear relations among the q-series which contain the derivation relations for a q-analogue of multiple zeta values due to Bradley. As a…

Number Theory · Mathematics 2019-06-04 Yoshihiro Takeyama

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

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

An explicit formula for the height-one multiple zeta values was proved by Kaneko and the second author. We give an alternative proof of this result and its generalization. We also prove its counterpart for the finite multiple zeta values.

Number Theory · Mathematics 2017-11-15 Hideki Murahara , Mika Sakata

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

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