Abstract

In this paper, we consider the zeta function Z(P,χ,s) associated with a polynomial P(X) in R[X₁,…,X_r] and χ = (χ₁,…,χ_r) with χ_j non-trivial Dirichlet characters, defined by

which is absolutely convergent for suficiently large Re s under some conditions on P(X). We shall prove that the special value Z(P,χ,−m) is completely determined by P^m(X) in a simple way. As an immediate application, we give a closed expression for sums of products of any number of generalized Bernoulli numbers.

Authors