On the analytic continuation of Dirichlet series

Abstract:

Given a continuable Dirichlet series, having as sequence of exponents $\{ {\lambda _n}\} _{n = 1}^\infty$, it is shown that any other Dirichlet series can be continued along the same paths away from its half plane of convergence provided that the two series have the same coefficients and that the difference of their exponents is eventually given by a function analytic at infinity evaluated at the ${\lambda _n}$.