On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series

Abstract

Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration admit a functional equation.