Values at non-positive integers of generalized Euler–Zagier multiple zeta-functions
Volume 193 / 2020
Acta Arithmetica 193 (2020), 109-131
MSC: Primary 11M32; Secondary 11M41.
DOI: 10.4064/aa171120-13-3
Published online: 17 January 2020
Abstract
We give new closed and explicit formulas for “multiple zeta values” at non-positive integers of generalized Euler–Zagier multiple zeta-functions. We first prove these formulas for a small convenient class of these multiple zeta-functions and then use the analyticity of the values on the parameters defining the multiple zeta-functions to deduce the formulas in the general case. Also, we prove an extension of “Raabe’s lemma” due to E. Friedman and A. Pereira (2007).
