Analog of Szegö's theorem for a class of Dirichlet series
type: Item
instance of: scholarly article
title: Analog of Szegö's theorem for a class of Dirichlet series
zbMATH Open document ID: 0592.30003
DOI: 10.1007/BF01161580
author: V. N. Kuznetsov
published in: Mathematical Notes
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 30B50
zbMATH DE Number: 3950921
zbMATH Keywords: meromorphic functions
zbMATH Keywords: Szegö's theorem
zbMATH Keywords: Dirichlet series
MaRDI profile type: Publication
cites work: Q3892486
full work available at URL: https://doi.org/10.1007/bf01161580
OpenAlex ID: W2943406063
description: scientific article; zbMATH DE number 3950921