Asymptotic estimate of the sum of a Dirichlet series on curves
Let \(F(s)\) be the sum of entire Dirichlet series \(\sum^\infty_{n =1} a_n\exp (\lambda_ns)\) where \(\sum^\infty_{n=1} {1\over\lambda^2_n} <\infty\) and let \(\gamma\) be a curve going to infinity so that if \(s\in\gamma\) and \(s\to \infty\) then \(Re(s)\to +\infty\). The author gives under general conditions an asymptotic estimate of \(F(s)\) on \(\gamma\).
scientific article; zbMATH DE number 1238023