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Extended double shuffle relations for multiple zeta values are obtained by the fact that any product of regularized multiple zeta values has two different representations, and the case of two-fold product is considered in general. In this…

Number Theory · Mathematics 2019-07-24 Tomoya Machide

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

We investigate linear relations among a class of iterated integrals on the Riemann sphere minus four points $0,1,z$ and $\infty$. Generalization of the duality formula and the sum formula for multiple zeta values to the iterated integrals…

Number Theory · Mathematics 2017-04-24 Minoru Hirose , Kohei Iwaki , Nobuo Sato , Koji Tasaka

This note is a compilation of related research on modular relations for multiple zeta values. Roughly speaking, modular relations are (homogeneous) linear relations of multiple zeta values of fixed weight whose coefficients are `originated'…

Number Theory · Mathematics 2023-09-18 Koji Tasaka

In this paper we give two idelic representations of the multiple zeta values - one using iterated integrals over the finite ideles and the other using iterated integrals over the idele class group. Each of the representations leads to a…

Number Theory · Mathematics 2014-09-30 Ivan Horozov

One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta functions are a generalization of the multiple zeta functions of…

Number Theory · Mathematics 2025-06-30 Maki Nakasuji , Yasuo Ohno , Wataru Takeda

In this paper, we investigate the shuffle product relations for Euler-Zagier multiple zeta functions as functional relations. To this end, we generalize the classical partial fraction decomposition formula and give two proofs. One is based…

Number Theory · Mathematics 2025-06-13 Nao Komiyama , Takeshi Shinohara

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

In this paper, we study the multiple $L$-values and the multiple zeta values of level $N$. We set up the algebraic framework for the double shuffle relations of the multiple zeta values of level $N$. Using the regularized double shuffle…

Number Theory · Mathematics 2021-03-08 Zhonghua Li , Zhenlu Wang

The shuffle product plays an important role in the study of multiple zeta values. This is expressed in terms of multiple integrals, and also as a product in a certain non-commutative polynomial algebra over the rationals in two…

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

We study a certain class of q-analogues of multiple zeta values, which appear in the Fourier expansion of multiple Eisenstein series. Studying their algebraic structure and their derivatives we propose conjectured explicit formulas for the…

Number Theory · Mathematics 2016-09-30 Henrik Bachmann

The derivation relations for multiple zeta values is proved by Ihara, Kaneko and Zagier. We prove its counterpart for finite multiple zeta values.

Number Theory · Mathematics 2016-02-29 Hideki Murahara

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

In this paper we use the generating functions and the double shuffle relations satisfied the multiple zeta values to derive some new families of identities.

Number Theory · Mathematics 2018-04-06 Haiping Yuan , Jianqiang Zhao

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

We construct a q-analogue of truncated version of symmetric multiple zeta values which satisfies the double shuffle relation. Using it, we define a q-analogue of symmetric multiple zeta values and see that it satisfies many of the same…

Number Theory · Mathematics 2023-06-28 Yoshihiro Takeyama

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 study a variant of multiple zeta values of level 2, which forms a subspace of the space of alternating multiple zeta values. This variant, which is regarded as the `shuffle counterpart' of Hoffman's `odd variant', exhibits nice…

Number Theory · Mathematics 2019-04-18 Masanobu Kaneko , Hirofumi Tsumura

It was shown in that harmonic numbers satisfy certain reciprocity relations, which are in particular useful for the analysis of the quickselect algorithm. The aim of this work is to show that a reciprocity relation from…

Combinatorics · Mathematics 2009-05-05 Helmut Prodinger , Markus Kuba

Shuffle algebra has been employed to give a proof of the duality theorem for multiple zeta-star values of height one.

Number Theory · Mathematics 2023-07-20 Nita Tamang , Pitu Sarkar