English
Related papers

Related papers: A note on $\mathcal{F}_n$-multiple zeta values

200 papers

In this paper, we study sum formulas for Schur multiple zeta values and give a generalization of the sum formulas for multiple zeta(-star) values. We show that for ribbons of certain types, the sum over all admissible Young tableaux of this…

Number Theory · Mathematics 2023-06-05 Henrik Bachmann , Shin-ya Kadota , Yuta Suzuki , Shuji Yamamoto , Yoshinori Yamasaki

We introduce an algebraic formulation of cyclic sum formulas for multiple zeta values and for multiple zeta-star values. We also present an algebraic proof of cyclic sum formulas for multiple zeta values and for multiple zeta-star values by…

Number Theory · Mathematics 2009-02-17 Tatsushi Tanaka , Noriko Wakabayashi

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

In this paper, we formally introduce the notion of Ap{\'e}ry-like sums and we show that every multiple zeta values can be expressed as a $\bf Z$-linear combination of them. We even describe a canonical way to do so. This allows us to put in…

Number Theory · Mathematics 2019-12-12 P. Akhilesh

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 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

We give three identities involving multiple zeta values of height one and of maximal height; an explicit formula for the height-one multiple zeta values, a regularized sum formula, and a sum formula for the multiple zeta values of maximal…

Number Theory · Mathematics 2019-02-20 Masanobu Kaneko , Mika Sakata

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

A typical formula of multiple zeta values is the sum formula which expresses a Riemann zeta value as a sum of all multiple zeta values of fixed weight and depth. Recently weighted sum formulas, which are weighted analogues of the sum…

Number Theory · Mathematics 2013-03-12 Tomoya Machide

We introduce and study a ``level two'' analogue of finite multiple zeta values. We give conjectural bases of the space of finite Euler sums as well as that of usual finite multiple zeta values in terms of these newly defined elements. A…

Number Theory · Mathematics 2021-09-28 Masanobu Kaneko , Takuya Murakami , Amane Yoshihara

Recently, Bradley studied partial sums of multiple q-zeta values and proved a duality result. In this paper, we present a generalization of his result.

Number Theory · Mathematics 2009-05-05 Gaku Kawashima

In this article, we study the multiple zeta functions (MZF) and some of its variants at identical arguments. Using the harmonic product, these functions can be expressed as polynomials in the Riemann zeta function. Firstly, we note that an…

Number Theory · Mathematics 2026-03-31 Pawan Singh Mehta

Recently, the author and Yamamoto invented a new proof of the duality for multiple zeta values. The technique is applicable in other series identities. In this article, we exhibit such proofs for some series identities.

Number Theory · Mathematics 2020-06-23 Shin-ichiro Seki

We introduce a $q$-analog of the multiple harmonic series commonly referred to as multiple zeta values. The multiple $q$-zeta values satisfy a $q$-stuffle multiplication rule analogous to the stuffle multiplication rule arising from the…

Quantum Algebra · Mathematics 2007-06-13 David M. Bradley

In this paper, we prove a new identity for values of the Hurwitz zeta function which contains as particular cases Koecher's identity for odd zeta values, the Bailey-Borwein-Bradley identity for even zeta values and many other interesting…

Number Theory · Mathematics 2012-07-19 Khodabakhsh Hessami Pilehrood , Tatiana Hessami Pilehrood

We study some classical identities for multiple zeta values and show that they still hold for zeta functions built on the zeros of an arbitrary function. We introduce the complementary zeta function of a system, which naturally occurs when…

Number Theory · Mathematics 2021-02-09 Tanay Wakhare , Christophe Vignat

This paper aims to study the $\mathbb{F}_q-$linear relations between interpolated $v-$adic multiple zeta values over function fields. We proved a universal family of linear relations of interpolated $v-$adic MZVs, which is conjectured to…

Number Theory · Mathematics 2019-12-24 Qibin Shen

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples,…

Number Theory · Mathematics 2020-11-11 Nikita Markarian

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