Asymptotic Dirichlet series in a strip

Abstract

In this paper a study is made of the asymptotic representation, by sums of exponentials of the form n=1m ane-nnz , of a function F(z) which is holomorphic in a strip. The fundamental theorem is to the effect that if a function F(z) is regular in a curvilinear strip, and is represented there in a generalized sense by a Dirichlet series (usually divergent) with given exponents, the coefficients of the Dirichlet series admit certain estimates (involving all the data)