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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 Ohno relation is a well known relation in the theory of multiple zeta values. Recently, Seki and Yamamoto introduced a connector method and gave its succinct proof. On the other hand, Igarashi obtained the generalization of the Ohno…

Number Theory · Mathematics 2020-12-02 Hideki Murahara , Tomokazu Onozuka

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 gives a large family of relations of the multiple zeta values. We shall show functional relations of generating functions of Ohno's relation. With these relations we present a new proof of Ohno's relation.

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

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

Parametrized multiple series are generalizations of the multiple zeta values introduced by Igarashi. In this work, we completely determine all the linear relations among these parameterized multiple series. Specifically, we prove the…

Number Theory · Mathematics 2021-11-29 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka

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

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 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

We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…

Number Theory · Mathematics 2012-10-31 Tomoya Machide

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 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

Ohno's relation is a well-known family of relations among multiple zeta values, which can naturally be regarded as a type of duality for a certain power series which we call an Ohno sum. In this paper, we investigate $\mathbb{Q}$-linear…

Number Theory · Mathematics 2019-10-18 Minoru Hirose , Hideki Murahara , Tomokazu Onozuka , Nobuo Sato

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

We prove the Ohno-type relation for the interpolated multiple zeta values, which was introduced first by Yamamoto. Same type results for finite multiple zeta values are also given. Moreover, these relations give the sum formula for…

Number Theory · Mathematics 2021-04-22 Minoru Hirose , Hideki Murahara , Masataka Ono

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

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

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

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 multiple zeta values and their generalizations from the point of view of Rota--Baxter algebras. We obtain a general framework for this purpose and derive relations on multiple zeta values from relations in Rota--Baxter algebras.

Number Theory · Mathematics 2014-10-14 Kurusch Ebrahimi-Fard , Li Guo
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