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We take another look at the so-called quasi-derivation relations in the theory of multiple zeta values, by giving a certain formula for the quasi-derivation operator. In doing so, we are not only able to prove the quasi-derivation relations…

Number Theory · Mathematics 2019-07-23 Masanobu Kaneko , Hideki Murahara , Takuya Murakami

We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties, that is, Fourier expansions, analytic continuations,…

Classical Analysis and ODEs · Mathematics 2014-09-09 Genki Shibukawa

We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision…

Number Theory · Mathematics 2014-06-10 Li Guo , Sylvie Paycha , Bin Zhang

We consider a cyclic analogue of multiple zeta values (CMZVs), which has two kinds of expressions; series and integral expression. We prove an `integral$=$series' type identity for CMZVs. By using this identity, we construct two classes of…

Number Theory · Mathematics 2018-07-04 Minoru Hirose , Hideki Murahara , Takuya Murakami

Interpolated multiple zeta values can be regarded as interpolation polynomials of multiple zeta values and multiple zeta-star values. In this paper, we give some algebraic relations of interpolated multiple zeta values, such as the…

Number Theory · Mathematics 2019-04-23 Zhonghua Li

The $t$-adic symmetric multiple zeta value is a generalization of the symmetric multiple zeta value from the perspective of the Kaneko-Zagier conjecture. In this paper, we introduce a further generalization with a new parameter $s$, which…

Number Theory · Mathematics 2023-11-02 Minoru Hirose , Hanamichi Kawamura

In this paper, we construct certain analogues of the Arakawa-Kaneko zeta functions. We prove functional relations between these functions and the Mordell-Tornheim multiple zeta functions. Furthermore we give some formulas among…

Number Theory · Mathematics 2016-03-15 Takuma Ito

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

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

In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.

Number Theory · Mathematics 2009-12-31 T. Kim

In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…

Number Theory · Mathematics 2012-11-08 Kazuhiro Onodera

In this paper, the extended double shuffle relations for interpolated multiple zeta values are established. As an application, Hoffman's relations for interpolated multiple zeta values are proved. Furthermore, a generating function for sums…

Number Theory · Mathematics 2017-03-30 Zhonghua Li , Chen Qin

We shall define the q-analogs of multiple zeta functions and multiple polylogarithms in this paper and study their properties, based on the work of Kaneko et al. and Schlesinger, respectively.

Quantum Algebra · Mathematics 2009-07-02 Jianqiang Zhao

We establish a new class of relations among the multiple zeta values \zeta(k_1,k_2,...,k_n), which we call the cyclic sum identities. These identities have an elementary proof, and imply the "sum theorem" for multiple zeta values. They also…

Quantum Algebra · Mathematics 2007-05-23 Michael E. Hoffman , Yasuo Ohno

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 study relations between multizeta values for function fields introduced by D. Thakur. The F_p-span of Thakur's multizeta values is an algebra (Thakur. Shuffle relations for function field multizeta values). In particular, the product…

Number Theory · Mathematics 2011-08-25 José Alejandro Lara Rodríguez

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

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

Colored multiple zeta values are special values of multiple polylogarithms evaluated at Nth roots of unity. In this paper, we define both the finite and the symmetrized versions of these values and show that they both satisfy the double…

Number Theory · Mathematics 2020-05-26 Johannes Singer , Jianqiang Zhao

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