Ohno-Zagier type relation for multiple $t$-values

Zhonghua Li; Yutong Song

Ohno-Zagier type relation for multiple $t$-values

Number Theory 2022-04-19 v1

Authors: Zhonghua Li , Yutong Song

Abstract

We study the Ohno-Zagier type relation for multiple $t$ -values and multiple $t$ -star values. We represent the generating function of sums of multiple $t$ -(star) values with fixed weight, depth and height in terms of the generalized hypergeometric function $\,_3F_2$ . As applications, we get a formula for the generating function of sums of multiple $t$ -(star) values of maximal height and a weighted sum formula for sums of multiple $t$ -(star) values with fixed weight and depth.

Keywords

multiple zeta values hypergeometric functions

Cite

@article{arxiv.2204.07785,
  title  = {Ohno-Zagier type relation for multiple $t$-values},
  author = {Zhonghua Li and Yutong Song},
  journal= {arXiv preprint arXiv:2204.07785},
  year   = {2022}
}

Comments

12 pages

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