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

Kwang-Wu Chen; Minking Eie; Yao Lin Ong

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

Number Theory 2023-04-19 v1

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

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.

Keywords

multiple zeta values zeta-star values symmetry duality zagier's formula

Cite

@article{arxiv.2304.08722,
  title  = {Some Symmetry and Duality Theorems on Multiple Zeta(-star) Values},
  author = {Kwang-Wu Chen and Minking Eie and Yao Lin Ong},
  journal= {arXiv preprint arXiv:2304.08722},
  year   = {2023}
}

Comments

14 pages. I would appreciate any constructive feedback and alternative perspectives on my paper. Thank you!

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

Abstract

Keywords

Cite

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