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

Kwang-Wu Chen; Minking Eie; Yao Lin Ong

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arXiv · 2304.08722

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

Kwang-Wu Chen·Minking Eie·Yao Lin Ong

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

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Kwang-Wu Chen, Minking Eie, Yao Lin Ong. 2023-04-18. Some Symmetry and Duality Theorems on Multiple Zeta(-star) Values. https://arxiv.org/abs/2304.08722

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