Eisenstein series whose Fourier coefficients are zeta functions of binary Hermitian forms

Abstract

In this paper we investigate a result of Ueno on the modularity of generating series associated to the zeta functions of binary Hermitian forms previously studied by Elstrodt et al. We improve his result by showing that the generating series are Eisenstein series. As a consequence we obtain an explicit formula for the special values of zeta functions associated with binary Hermitian forms.

Accepted for publication in the Proceedings of the American Mathematical Society. 10pp