On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series

H. Ishikawa; J. M. Thuswaldner

doi:10.1007/BF02941522

On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series

H. Ishikawa^*, J. M. Thuswaldner

^*Corresponding author for this work

Joint Institute of Teacher Education

Research output: Contribution to journal › Article › peer-review

Abstract

Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration admit a functional equation.

Original language	English
Pages (from-to)	11-32
Number of pages	22
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	74
Issue number	1
DOIs	https://doi.org/10.1007/BF02941522
State	Published - 2004/12

Keywords

Dirichlet series
Functional equation
Laurent series

ASJC Scopus subject areas

General Mathematics

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10.1007/BF02941522

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title = "On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series",

abstract = "Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration admit a functional equation.",

keywords = "Dirichlet series, Functional equation, Laurent series",

author = "H. Ishikawa and Thuswaldner, {J. M.}",

note = "Funding Information: 2000 Mathematics Subject Classification. l lM41, 30B50, 41A60. Key words and phrases, Dirichlet series, Laurent series, functional equation. The second author was supported by the FWF project $3810.",

year = "2004",

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AU - Ishikawa, H.

AU - Thuswaldner, J. M.

N1 - Funding Information: 2000 Mathematics Subject Classification. l lM41, 30B50, 41A60. Key words and phrases, Dirichlet series, Laurent series, functional equation. The second author was supported by the FWF project $3810.

PY - 2004/12

Y1 - 2004/12

N2 - Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration admit a functional equation.

AB - Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration admit a functional equation.

KW - Dirichlet series

KW - Functional equation

KW - Laurent series

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U2 - 10.1007/BF02941522

DO - 10.1007/BF02941522

M3 - 学術論文

AN - SCOPUS:51349136604

SN - 0025-5858

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JO - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

JF - Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg

IS - 1

ER -

On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series

Abstract

Keywords

ASJC Scopus subject areas

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