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Some Abelian results for Dirichlet series

Published online by Cambridge University Press:  26 February 2010

W. E. Briggs
W. E. Briggs
Affiliation:
University of Colorado. University College, London
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Extract

If f(s) is the analytic function defined by the Dirichlet series and if where 0 ≤ b < 1, then the series converges for Re s > 1 and f(s) is regular in the half plane Re s > b except for a simple pole with residue C ≠ 0 at a s = 1. Thus f(s) has a Laurent expansion at s = 1 and it has been shown [1] that under these conditions

where

Type
Research Article
Information
Mathematika , Volume 9 , Issue 1 , June 1962 , pp. 49 - 53
Copyright
Copyright © University College London 1962

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References

1.Briggs, W. E. and Buschman, R. G., “The power series coefficients of functions defined by Dirichlet series”, Illinois J. of Math., 5 (1961), 43–44.CrossRefGoogle Scholar