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On the Non-Vanishing of a Certain Class of Dirichlet Series

Published online by Cambridge University Press:  20 November 2018

Sridhar Narayanan
Sridhar Narayanan*
Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, H3A 2K6
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Abstract

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In this paper, we consider Dirichlet series with Euler products of the form F(s) = Πp in > 1, and which are regular in ≥ 1 except for a pole of order m at s = 1. We establish criteria for such a Dirichlet series to be nonvanishing on the line of convergence. We also show that our results can be applied to yield non-vanishing results for a subclass of the Selberg class and the Sato-Tate conjecture.

Keywords

Primary: 11MxxSecondary: 11M41
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 3 , 01 September 1997 , pp. 364 - 369
Copyright
Copyright © Canadian Mathematical Society 1997

References

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