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

2020/09/22 by Ce Xu, Jianqiang Zhao, Xu, Ce +1 · 1 citation
Mathematics · #11B39 #11G55 #11M06 #11M32 #11M35 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B39 #msc:11G55 #msc:11M06 #msc:11M32 #msc:11M35

paper · pdf · doi:10.48550/arxiv.2009.10774

33 page

arxiv created 2020/09/22 · arxiv updated 2020/09/24

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≥ 1} form the tribonacci sequence 1, 2, 4, 7, 13, ....

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