Weighted sum formula of multiple $L$-values and its applications

Li, Zhonghua; Wang, Zhenlu

doi:10.48550/arxiv.2102.07184

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2022

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“…Z. Li and Z. Wang studied the algebraic framework for the double shuffle relations of multiple zeta values of level N and gave sum formulas and weighted sum formulas of double zeta values of level 2 and 3 in [15]. Two variants of multiple zeta values of level 2 called the multiple t-values [8] and the multiple T -values [10] have been studied recent years, see for example [3,8,10,14,16,20].…”

Section: Introductionmentioning

confidence: 99%

Relations of multiple $t$-values of general level

Li¹,

Wang²

2022

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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 3 F 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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