English
Related papers

Related papers: On the duality formula for parametrized multiple s…

200 papers

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

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

The multiple zeta values are generalizations of the values of the Riemann zeta function at positive integers. They are known to satisfy a number of relations, among which are the cyclic sum formula. The cyclic sum formula can be stratified…

Number Theory · Mathematics 2011-03-11 Shingo Saito , Tatsushi Tanaka , Noriko Wakabayashi

Euler's sum formula and its multi-variable and weighted generalizations form a large class of the identities of multiple zeta values. In this paper we prove a family of identities involving Bernoulli numbers and apply them to obtain…

Number Theory · Mathematics 2015-10-15 Li Guo , Peng Lei , Jianqiang Zhao

In this paper we introduce and study double tails of multiple zeta values. We show, in particular, that they satisfy certain recurrence relations and deduce from this a generalization of Euler's classical formula…

Number Theory · Mathematics 2021-05-27 P. Akhilesh

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

In this paper, we discuss the parity result for multiple Dirichlet series which contains some special values of multiple zeta functions as special cases, Mordell--Tornheim type of multiple zeta values, zeta values of the root systems and so…

Number Theory · Mathematics 2019-09-27 Shin-ya Kadota

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is…

Number Theory · Mathematics 2016-04-05 Masanobu Kaneko , Fumi Sakurai , Hirofumi Tsumura

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

Following Bachmann's recent work on bi-brackets and multiple Eisenstein series, Zudilin introduced the notion of multiple q-zeta brackets, which provides a q-analog of multiple zeta values possessing both shuffle as well as quasi-shuffle…

Number Theory · Mathematics 2016-08-16 Kurusch Ebrahimi-Fard , Dominique Manchon , Johannes Singer

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

The sum formula for $q$-multiple zeta values is a well-known relation. In this paper, we present its generalization for the $q$-multiple zeta function.

Number Theory · Mathematics 2026-03-03 Anju Yokoi

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 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

Multiple q-zeta values are a 1-parameter generalization (in fact, a q-analog) of the multiple harmonic sums commonly referred to as multiple zeta values. These latter are obtained from the multiple q-zeta values in the limit as q tends to…

Quantum Algebra · Mathematics 2007-10-31 David M. Bradley

We give an explicit formula for the well-known parity result for multiple zeta values as an application of the multitangent functions.

Number Theory · Mathematics 2024-10-03 Minoru Hirose

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

In this paper we consider a family of multiple Hurwitz zeta values with bi-indices parameterized by $\mu$ with $\Ree(\mu)>0$. These values are equipped with both the $\mu$-stuffle product from their series definition and the shuffle product…

Number Theory · Mathematics 2024-02-20 Jia Li , Jianqiang Zhao

It is conjectured that the regularized double shuffle relations give all algebraic relations among the multiple zeta values, and hence all other algebraic relations should be deduced from the regularized double shuffle relations. In this…

Number Theory · Mathematics 2019-08-15 Zhonghua Li , Chen Qin

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