On the sum relation of multiple Hurwitz zeta functions

2016/09/06 by Chung, Chan-Liang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.01362

Abstract

In this paper we shall define a special-valued multiple Hurwitz zeta functions, namely the multiple t-values t(\boldsymbolα) and define similarly the multiple star t-values as t^⋆(\boldsymbolα). Then we consider the sum of all such multiple (star) t-values of fixed depth and weight with even argument and prove that such a sum can be evaluated when the evaluations of t(\2m\ⁿ) and t^⋆(\2m\ⁿ) are clear. We give the evaluations of them in terms of the classical Euler numbers through their generating functions.

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