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Bowman and Bradley proved an explicit formula for the sum of multiple zeta values whose indices are the sequence (3,1,3,1,...,3,1) with a number of 2's inserted. Kondo, Saito and Tanaka considered the similar sum of multiple zeta-star…

Number Theory · Mathematics 2012-03-07 Shuji Yamamoto

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

We exhibit the double q-shuffle structure for the qMZVs recently introduced by Y. Ohno, J. Okuda and W. Zudilin.

Number Theory · Mathematics 2019-02-20 Jaime Castillo Medina , Kurusch Ebrahimi-Fard , Dominique Manchon

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

In recent years, a variety of variants of multiple zeta values (MZVs) have been defined and studied. One way to produce these variants is to restrict the indices in the definition of MZVs to some fixed parity pattern, which include…

Number Theory · Mathematics 2024-09-27 Jianqiang Zhao

The multiple zeta values are multivariate generalizations of the values of the Riemann zeta function at positive integers. The Bowman-Bradley theorem asserts that the multiple zeta values at the sequences obtained by inserting a fixed…

Number Theory · Mathematics 2014-06-11 Shingo Saito , Noriko Wakabayashi

We prove an identity for multiple zeta star values, which generalises some identities due to Imatomi, Tanaka, Tasaka and Wakabayashi. This identity gives an analogue of cyclic insertion type identities, for multiple zeta star values, and…

Number Theory · Mathematics 2018-06-27 Steven Charlton

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

In this paper, we establish some expressions of Mneimneh-type binomial sums involving multiple harmonic-type sums in terms of finite sums of Stirling numbers, Bell numbers and some related variables. In particular, we present some new…

Number Theory · Mathematics 2024-03-29 Ende Pan , Ce Xu

We present explicit formulas for Hecke eigenforms as linear combinations of q-analogues of modified double zeta values. As an application, we obtain period polynomial relations and sum formulas for these modified double zeta values. These…

Number Theory · Mathematics 2018-08-30 Henrik Bachmann

Bowman and Bradley obtained a remarkable formula among multiple zeta values. The formula states that the sum of multiple zeta values for indices which consist of the shuffle of two kinds of the strings $\{1,3,\ldots,1,3\}$ and…

Number Theory · Mathematics 2019-05-21 Hideki Murahara , Tomokazu Onozuka , Shin-ichiro Seki

In this paper, we obtain a restricted decomposition formula for interpolated multiple zeta values using t-stuffle product. We then derive a recursive formula of t-stuffle product, which also provides a route to the same formula. In both…

Number Theory · Mathematics 2024-11-12 Pitu Sarkar , Nita Tamang

Maesaka, Seki, and Watanabe recently discovered an equality called the MSW formula. This paper provides a $q$-analogue of the MSW formula. It discusses the new proof of the duality relation for finite multiple harmonic $q$-series at…

Number Theory · Mathematics 2024-08-30 Yuto Tsuruta

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 study special values of finite multiple harmonic q-series at roots of unity. These objects were recently introduced by the authors and it was shown that they have connections to finite and symmetric multiple zeta values and the…

Number Theory · Mathematics 2018-07-03 Henrik Bachmann , Yoshihiro Takeyama , Koji Tasaka

We discuss the shuffle product of the Schur multiple zeta values, which are the special values of Schur multiple zeta functions. We first define $2$-labeled Schur posets to generalize Yamamoto's integral expression of the multiple zeta…

Number Theory · Mathematics 2022-01-12 Maki Nakasuji , Wataru Takeda

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

Kawashima's relation is conjecturally one of the largest classes of relations among multiple zeta values. Gaku Kawashima introduced and studied a certain Newton series, which we call the Kawashima function, and deduced his relation by…

Number Theory · Mathematics 2020-12-01 Masanobu Kaneko , Ce Xu , Shuji Yamamoto

Through the application of an evaluation technique based on cyclotomic multiple zeta values recently due to Au, we solve open problems on inverse binomial series that were included in a 2010 analysis textbook by Chen.

Classical Analysis and ODEs · Mathematics 2024-09-04 John M. Campbell , M. Lawrence Glasser , Yajun Zhou

One of the most interesting formulas for multiple zeta values is the sum formula proved by Granville and Zagier independently in 1990s. Many variations and generalizations of it have been found since then. In this paper, we will provide a…

Number Theory · Mathematics 2025-08-06 Jianqiang Zhao