Proof of Kaneko-Tsumura conjecture on triple T-values

被引：2

作者：

Berger, Sasha ^{[1
]}

Chandra, Aarav ^{[1
]}

Jain, Jasper ^{[1
]}

Xu, Daniel ^{[1
]}

Xu, Ce ^{[2
]}

Zhao, Jianqiang ^{[1
]}

机构：

[1] Bishops Sch, Dept Math, La Jolla, CA 92037 USA

[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年 / 19卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Euler sum; multiple zeta value; weighted sum formula; multiple T-value; GENERATING FUNCTION; ZETA VALUES; SUM FORMULA;

D O I：

10.1142/S1793042123500239

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Many Q-linear relations exist between multiple zeta values, the most interesting of which are the weighted sum formulas. In this paper, we generalize these to Euler sums and Kaneko and Tsumura's multiple T-values, a variant of the multiple zeta values, by considering generating functions of the Euler sums. Through this approach, we are able to re-prove a few known formulas, confirm a conjecture of Kaneko and Tsumura on triple T-values, and discover many new identities.

引用

页码：495 / 510

页数：16

共 10 条

[1] Double zeta values and modular forms [J].