A note on the gaps between zeros of Epstein's zeta-functions on the critical line

Stephan Baier; Srinivas Kotyada; Usha Keshav Sangale

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arXiv · 1602.06069

A note on the gaps between zeros of Epstein's zeta-functions on the critical line

Stephan Baier·Srinivas Kotyada·Usha Keshav Sangale

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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. 2016-02-19. A note on the gaps between zeros of Epstein's zeta-functions on the critical line. https://arxiv.org/abs/1602.06069

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