Work

Some Symmetry and Duality Theorems on Multiple Zeta(-Star) Values

Year: 2024

Type: article

Abstract: In this paper, we provide a symmetric formula and a duality formula relating multiple zeta values and zeta-star values. We find that the summation ∑a+b=r−1(−1)aζ★(a+2,{2}p−1)ζ★({1}b+1,{2}q) equals ζ★({2}p,{1}r,{2}q)+(−1)r+1ζ★({2}q,r+2,{2}p−1). With the help of this equation and Zagier’s ζ★({2}p,3,{2}q) formula, we can easily determine ζ★({2}p,1,{2}q) and several interesting expressions.

Source: Mathematics

DOI: 10.3390/math12203292

Authors: Kwang-Wu Chen, Minking Eie, Yao Lin Ong

Institutions: University of Taipei, National Chung Cheng University, Chang Jung Christian University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: Ministry of Science and Technology, Taiwan