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An Inculsion Theorem for Dirichlet Series

Published online by Cambridge University Press:  20 November 2018

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

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It is shown that under certain conditions the asymptotic relationship

between two Dirichlet series implies the same relationship with λn replaced by log λn.

Keywords

40D2540G10
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 32 , Issue 4 , 01 December 1989 , pp. 479 - 481
Copyright
Copyright © Canadian Mathematical Society 1989

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.Google Scholar
2. Borwein, D., Tauberian and other theorems concerning Dirichlet's series with non-negative coefficients, Math. Proc. Camb. Phil. Soc, 102 (1987), 517–532.Google Scholar
3. Hardy, G. H., Divergent Series (Oxford University Press, 1949).Google Scholar