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

2023/04/18 by Chen, Kwang-Wu, Eie, Minking, Ong, Yao Lin
#11M32 #33B15 #FOS: Mathematics #Number Theory (math.NT) #Secondary: 05A15

paper · doi:10.48550/arxiv.2304.08722

Abstract

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 ζ^⋆(\2\^p,3,\2\^q), we employ our theorems to establish a formula for computing ζ^⋆(\2\^p,1,\2\^q) for any positive integers p and q, along with other formulas of interest.

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