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Related papers: Ohno-Zagier type relation for multiple $t$-values

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We study the relations of multiple $t$-values of general level. The generating function of sums of multiple $t$-(star) values of level $N$ with fixed weight, depth and height is represented by the generalized hypergeometric function…

Number Theory · Mathematics 2022-11-01 Zhonghua Li , Zhenlu Wang

We give an explicit representation for the sums of multiple zeta-star values of fixed weight and height in terms of Riemann zeta values.

Number Theory · Mathematics 2007-05-23 Takashi Aoki , Yasuo Ohno

Ohno's relation states that a certain sum, which we call an Ohno type sum, of multiple zeta values remains unchanged if we replace the base index by its dual index. In view of Oyama's theorem concerning Ohno type sums of finite and…

Number Theory · Mathematics 2019-05-14 Minoru Hirose , Hideki Murahara , Shingo Saito

In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple $t$-values $t(\boldsymbol{\alpha})$ and define similarly the multiple star $t$-values as $t^{\star}(\boldsymbol{\alpha})$. Then we consider…

Number Theory · Mathematics 2016-09-07 Chan-Liang Chung

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

We study generating functions for multiple zeta star values in general form. These generating functions provide a connection between multiple zeta star values and multiple Euler sums, which allows us to express each multiple zeta star value…

Number Theory · Mathematics 2019-05-21 Khodabakhsh Hessami Pilehrood , Tatiana Hessami Pilehrood

In this paper, we study the generating functions of multiple $t$-star values with an arbitrary number of blocks of twos, which are based on the results of the corresponding generating functions of multiple $t$-harmonic star sums. These…

Number Theory · Mathematics 2022-12-20 Zhonghua Li , Lu Yan

In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height $\leq 2$ and the evaluation of…

Number Theory · Mathematics 2022-02-09 Kwang-Wu Chen , Minking Eie

In this paper, we introduce the interpolated multiple $t$-values of general level and represent a generating function for sums of interpolated multiple $t$-values of general level with fixed weight, depth, and height in terms of a…

Number Theory · Mathematics 2025-04-22 Zhonghua Li , Zhenlu Wang

The sum formulas for multiple zeta(-star) values and symmetric multiple zeta(-star) values bear a striking resemblance. We explain the resemblance in a rather straightforward manner using an identity that involves the Schur multiple zeta…

Number Theory · Mathematics 2020-11-10 Minoru Hirose , Hideki Murahara , Shingo Saito

Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of…

Number Theory · Mathematics 2017-10-12 Zhonghua Li , Noriko Wakabayashi

In this paper, we study the explicit expressions of multiple t-star values with an arbitrary number of blocks of twos of general level. We give an expression of a generating function of such values, which generalizes the results for…

Number Theory · Mathematics 2023-12-14 Zhonghua Li , Lu Yan

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

We study multiple zeta values (MZVs) from the viewpoint of zeta-functions associated with the root systems which we have studied in our previous papers. In fact, the $r$-ple zeta-functions of Euler-Zagier type can be regarded as the…

Number Theory · Mathematics 2016-04-29 Yasushi Komori , Kohji Matsumoto , Hirofumi Tsumura

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 prove a kind of integral expressions for finite multiple harmonic sums and multiple zeta-star values. Moreover, we introduce a class of multiple integrals, associated with some combinatorial data (called 2-labeled posets). This class…

Number Theory · Mathematics 2014-05-27 Shuji Yamamoto

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 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

In this paper we establish several recurrence relations about Euler-Ap\'ery type multiple zeta star values and a parametric variant of it by using the method of iterated integrals. Then using the formulas obtained, we find the explicit…

Number Theory · Mathematics 2025-08-06 Ce Xu , Jianqiang Zhao

We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between…

Number Theory · Mathematics 2025-07-29 Shuji Yamamoto
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