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A Tauberian theorem concerning Dirichlet series

Published online by Cambridge University Press:  04 October 2011

David Borwein
David Borwein
Affiliation:
Department of Mathematics, University of Western Ontario, London, Ontario, Canada N6A 5B7
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Abstract

It is shown that under certain general Tauberian conditions the asymptotic relationship

between two Dirichlet series implies the asymptotic relationship

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 481 - 484
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

[1] Borwein, D.. Tauberian conditions for the equivalence of weighted mean and power series methods of summability. Canad. Math. Bull. 24 (1981), 309–316.CrossRefGoogle Scholar
[2] Borwein, D.. Tauberian and other theorems concerning Dirichlet's series with non-negative coefficients. Math. Proc. Cambridge Philos. Soc. 102 (1987), 517–532.CrossRefGoogle Scholar
[3] Borwein, D.. Tauberian theorems concerning Laplace transforms and Dirichlet series. Arch. Math. (Basel), (to appear).Google Scholar
[4] Tietz, H.. Tauberian theorems of Jp → Mp-type. Math. J. Okayama Univ. (to appear).Google Scholar