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

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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.

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Author information

Correspondence to H. Ishikawa or J. M. Thuswaldner.

Additional information

The second author was supported by the FWF project S381O.

J. Michaliček

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Ishikawa, H., Thuswaldner, J.M. On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series. Abh.Math.Semin.Univ.Hambg. 74, 11–32 (2004). https://doi.org/10.1007/BF02941522

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2000 Mathematics Subject Classification

  • 11M41
  • 30B50
  • 41A60

Key words and phrases

  • Dirichlet series
  • Laurent series
  • functional equation