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

Stephan Baier; Srinivas Kotyada; Usha Keshav Sangale

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

Number Theory 2017-03-13 v2

Authors: Stephan Baier , Srinivas Kotyada , Usha Keshav Sangale

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).

Keywords

Epstein zeta function critical line zeros gaps between zeros binary quadratic form analytic number theory zeta function zeros number theory

Cite

@article{arxiv.1602.06069,
  title  = {A note on the gaps between zeros of Epstein's zeta-functions on the critical line},
  author = {Stephan Baier and Srinivas Kotyada and Usha Keshav Sangale},
  journal= {arXiv preprint arXiv:1602.06069},
  year   = {2017}
}

Comments

17 pages, major revisions, expanded version of the earlier draft, to appear in Functiones et Approximatio

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

Abstract

Keywords

Cite

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