Laurent expansion of Dirichlet series. II
type: Item
instance of: scholarly article
title: Laurent expansion of Dirichlet series. II
zbMATH Open document ID: 0605.30004
DOI: 10.1007/BF01302705
author: U. Balakrishnan
published in: Monatshefte für Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178308
review text: [For part I see the author in Bull. Aust. Math. Soc. 33, 351-357 (1986; Zbl 0578.30003).] Let \(f(s)=\sum b_ na_ n^{-s}\) be a Dirichlet series, with appropriate conditions on \(a_ n\) and \(b_ n\), convergent in Re s\(>\lambda\) (\(\geq 1)\) and having an analytic continuation at least in Re s\(>0\) with a possible pole at \(s=\lambda\). Suppose \(f(\sigma +it)\) grows slower than a convenient power of t as \(t\to \infty\), we obtain the Laurent coefficients in the expansion of f(s) at \(s=\lambda\). The conditions mentioned above are general enough to cover a good class of Dirichlet series.
Mathematics Subject Classification ID: 30B50
Mathematics Subject Classification ID: 11M35
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 3977348
zbMATH Keywords: Riemann zeta function
zbMATH Keywords: Dedekind zeta function
zbMATH Keywords: Dirichlet series
MaRDI profile type: Publication
cites work: Laurent expansion of Dirichlet series
cites work: The power series coefficients of functions defined by Dirichlet series
cites work: Generalised Euler constants
description: scientific article; zbMATH DE number 3977348