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Related papers: Note on relations among multiple zeta-star values

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Ohno's relation is a generalization of both the sum formula and the duality formula for multiple zeta values. Oyama gave a similar relation for finite multiple zeta values, defined by Kaneko and Zagier. In this paper, we prove relations of…

Number Theory · Mathematics 2020-06-26 Minoru Hirose , Kohtaro Imatomi , Hideki Murahara , Shingo Saito

The main goal of this article is to present an elementary proof of Ramanujan's identity for odd zeta values. Our proof solely relies on a Mittag-Leffler type expansion for hyperbolic cotangent function and Euler's identity for even zeta…

Number Theory · Mathematics 2022-02-04 Sarth Chavan

Multiple zeta values (MZVs) are real numbers which are defined by certain multiple series. Recently, many people have researched for relations among them and many relations are well known. In this paper, we get a new relation among them…

Number Theory · Mathematics 2015-12-29 Shin-ya Kadota

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

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

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 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 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 evaluate several classes of high weight hypergeometric series via Multiple Zeta Values.

Number Theory · Mathematics 2020-09-29 Ming Hao Zhao

We prove an easy but interesting result about the linear independence of multiple zeta values of different weights.

Number Theory · Mathematics 2007-05-23 Sergey Zlobin

We obtain a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue. The weight coefficients are given by (symmetric) polynomials of…

Number Theory · Mathematics 2018-11-02 Zhonghua Li , Chen Qin

In this paper, we provide a symmetric formula and a duality formula relating multiple zeta values and zeta-star values. Leveraging Zagier's formula for computing $\zeta^\star(\{2\}^p,3,\{2\}^q)$, we employ our theorems to establish a…

Number Theory · Mathematics 2023-04-19 Kwang-Wu Chen , Minking Eie , Yao Lin Ong

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

Recently, Maesaka, Seki and Watanabe discovered a surprising equality between multiple harmonic sums and certain Riemann sums which approximate the iterated integral expression of the multiple zeta values. In this paper, we describe the…

Number Theory · Mathematics 2025-04-11 Shuji Yamamoto

Some combinatorial aspects of relations between multiple zeta values of depths 2 and 3 and period polynomials are discussed.

Number Theory · Mathematics 2020-05-18 Ding Ma , Koji Tasaka

In this note we introduce multi-interpolated multiple zeta values. We provide a basic decomposition of these objects involving ordered partitions. We also obtain identities for special instances of multi-interpolated multiple zeta values…

Combinatorics · Mathematics 2022-02-04 Markus Kuba

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 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

In this paper, we investigate three general forms of multiple zeta(-star) values. We use these values to give three new sum formulas for multiple zeta(-star) values with height $\leq 2$ and the evaluation of…

Number Theory · Mathematics 2022-02-09 Kwang-Wu Chen , Minking Eie

In this paper, we study the evaluation formulas of the interpolated multiple zeta values and the interpolated multiple $t$-values with indices involving $1,2,3$. To get these evaluations, we derive the corresponding algebraic relations in…

Number Theory · Mathematics 2024-04-24 Zhonghua Li , Zhenlu Wang