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

Ce Xu; Jianqiang Zhao

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

Number Theory 2020-09-24 v1

Authors: Ce Xu , Jianqiang Zhao

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 $\psi$ -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, ....

Keywords

multiple zeta values exponential sums

Cite

@article{arxiv.2009.10774,
  title  = {Alternating Multiple $T$-Values: Weighted Sums, Duality, and Dimension Conjecture},
  author = {Ce Xu and Jianqiang Zhao},
  journal= {arXiv preprint arXiv:2009.10774},
  year   = {2020}
}

Comments

33 page

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

Abstract

Keywords

Cite

Comments

Related papers