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December 2017 A note on the gaps between zeros of Epstein's zeta-functions on the critical line
Stephan Baier, Srinivas Kotyada, Usha Keshav Sangale
Funct. Approx. Comment. Math. 57(2): 235-253 (December 2017). DOI: 10.7169/facm/1630

Abstract

It is proved that Epstein's zeta-function $\zeta_{Q}(s)$, related to a positive definite integral binary quadratic form, has a zero $1/2 + i\gamma$ with $ T \leq \gamma \leq T + T^{{3/7} +\varepsilon} $ for sufficiently large positive numbers $T$. This is an improvement of the result by M. Jutila and K. Srinivas (Bull. London Math. Soc. 37 (2005) 45--53).

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Stephan Baier. Srinivas Kotyada. Usha Keshav Sangale. "A note on the gaps between zeros of Epstein's zeta-functions on the critical line." Funct. Approx. Comment. Math. 57 (2) 235 - 253, December 2017. https://doi.org/10.7169/facm/1630

Information

Published: December 2017
First available in Project Euclid: 28 March 2017

zbMATH: 06864173
MathSciNet: MR3732897
Digital Object Identifier: 10.7169/facm/1630

Subjects:
Primary: 11E45
Secondary: 11M41

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.57 • No. 2 • December 2017
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