Functiones et Approximatio Commentarii Mathematici

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

Stephan Baier, Srinivas Kotyada, and 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).

Article information

Source
Funct. Approx. Comment. Math., Volume 57, Number 2 (2017), 235-253.

Dates
First available in Project Euclid: 28 March 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1490688026

Digital Object Identifier
doi:10.7169/facm/1630

Mathematical Reviews number (MathSciNet)
MR3732897

Zentralblatt MATH identifier
06864173

Subjects
Primary: 11E45: Analytic theory (Epstein zeta functions; relations with automorphic
Secondary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72}

Keywords
Epstein's zeta-function Hardy's theorem gaps between consecutive zeros

Citation

Baier, Stephan; Kotyada, Srinivas; Sangale, Usha Keshav. A note on the gaps between zeros of Epstein's zeta-functions on the critical line. Funct. Approx. Comment. Math. 57 (2017), no. 2, 235--253. doi:10.7169/facm/1630. https://projecteuclid.org/euclid.facm/1490688026


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References

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