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We establish Ohno-type identities for multiple harmonic ($q$-)sums which generalize Hoffman's identity and Bradley's identity. Our result leads to a new proof of the Ohno-type relation for $\mathcal{A}$-finite multiple zeta values recently…

Number Theory · Mathematics 2018-08-09 Shin-ichiro Seki , Shuji Yamamoto

We prove a new class of relations among multiple zeta values (MZV's) which contains Ohno's relation. We also give the formula for the maximal number of independent MZV's of fixed weight, under our new relations. To derive our formula for…

Number Theory · Mathematics 2009-01-28 Gaku Kawashima

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

We study the Ohno-Zagier type relation for multiple $t$-values and multiple $t$-star values. We represent the generating function of sums of multiple $t$-(star) values with fixed weight, depth and height in terms of the generalized…

Number Theory · Mathematics 2022-04-19 Zhonghua Li , Yutong Song

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

We study a polynomial interpolation of finite multiple zeta and zeta-star values with variable $t$, which is an analogue of interpolated multiple zeta values introduced by Yamamoto. We introduce several relations among them and, in…

Number Theory · Mathematics 2020-08-25 Hideki Murahara , Masataka Ono

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 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

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

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

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

We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV's). In the limit q->1, it turns into Kawashima's relation for multiple zeta values. As a corollary we find that qMZV's satisfy the linear relation…

Number Theory · Mathematics 2010-08-05 Yoshihiro Takeyama

We present a new "integral=series" type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear…

Number Theory · Mathematics 2016-11-15 Masanobu Kaneko , Shuji Yamamoto

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

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 this paper, we give a formula that connects two variants of multiple zeta values; multitangent functions and symmetric multiple zeta values. As an application of this formula, we give two results. First, we prove Bouillot's conjecture on…

Number Theory · Mathematics 2024-02-22 Minoru Hirose

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

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

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 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