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arXiv · 2210.16854

Relations of multiple $t$-values of general level

Zhonghua Li·Zhenlu Wang
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Abstract

We study the relations of multiple $t$-values of general level. The generating function of sums of multiple $t$-(star) values of level $N$ with fixed weight, depth and height is represented by the generalized hypergeometric function $_3F_2$, which generalizes the results for multiple zeta(-star) values and multiple $t$-(star) values. As applications, we obtain formulas for the generating functions of sums of multiple $t$-(star) values of level $N$ with height one and maximal height and a weighted sum formula for sums of multiple $t$-(star) values of level $N$ with fixed weight and depth. Using the stuffle algebra, we also get the symmetric sum formulas and Hoffman's restricted sum formulas for multiple $t$-(star) values of level $N$. Some evaluations of multiple $t$-star values of level $2$ with one-two-three indices are given.

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Zhonghua Li, Zhenlu Wang. 2022-10-30. Relations of multiple $t$-values of general level. https://arxiv.org/abs/2210.16854

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