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arXiv · 2009.10774

Alternating Multiple $T$-Values: Weighted Sums, Duality, and Dimension Conjecture

Ce Xu·Jianqiang Zhao
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Abstract

In this paper, we define some weighted sums of the alternating multiple $T$-values (AMTVs), and study several duality formulas for them by using the tools developed in our previous papers. Then we introduce the alternating version of the convoluted $T$-values and Kaneko-Tsumura $ψ$-function, which are proved to be closely related to the AMTVs. At the end of the paper, we study the $\Q$-vector space generated by the AMTVs of any fixed weight $w$ and provide some evidence for the conjecture that their dimensions $\{d_w\}_{w\ge 1}$ form the tribonacci sequence 1, 2, 4, 7, 13, ....

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Ce Xu, Jianqiang Zhao. 2020-09-22. Alternating Multiple $T$-Values: Weighted Sums, Duality, and Dimension Conjecture. https://arxiv.org/abs/2009.10774

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