A functional relation for Tornheim's double zeta functions

Abstract

KAZUHIRO ONODERAAbstract. In this paper, we generalize the partial fraction decomposition which is fundamen-tal in the theory of multiple zeta values, and prove a relation between Tornheim’s double zetafunctions of three complex variables. As applications, we give new integral representations ofseveral zeta functions, an extension of the parity result to the whole domain of convergence,concrete expressions of Tornheim’s double zeta function at non-positive integers and some re-sults for the behavior of a certain Witten’s zeta function at each integer. As an appendix, weshow a functional equation for Euler’s double zeta function.