Analog of Szegö's theorem for a class of Dirichlet series
The following analogue of Szegö's theorem on the periodicity of coefficients of a power series is obtained. Theorem. For a Dirichlet series \(\sum a_ nn^{-s}\) the following conditions are equivalent: 1) Starting from a certain number, the coefficients \(a_ n\) are periodic. b) The function f(s) is meromorphic with possibly a single simple pole at the point \(s=1\), and satisfies the following condition on the growth of its modulus: \[ | f(s)(s-1)| <ce^{| s| \ell n| s| +A| s|} \] where \(A>0\) is a constant.
scientific article; zbMATH DE number 3950921