Weighted Sums of Euler Sums and Other Variants of Multiple Zeta Values

Sasha Berger, Aarav Chandra, Jasper Jain, Daniel Xu, Ce Xu, J. Zhao

Published 2020-11-04Version 1

Many $\mathbb{Q}$-linear relations exist between multiple zeta values, the most interesting ones of which are various weighted sum formulas. In this paper, we generalized these to Euler sums and some other variants of multiple zeta values by considering the 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.