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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The second author was supported by the FWF project S381O.
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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
2000 Mathematics Subject Classification
Key words and phrases
- Dirichlet series
- Laurent series
- functional equation