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

2016/02/19 by Stephan Baier, Baier, Stephan, Srinivas Kotyada +4
Mathematics · #11E45 #11M41 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #math.NT #msc:11E45 #msc:11M41

paper · pdf · doi:10.48550/arxiv.1602.06069

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

openalex publication_date 2016/02/19 · arxiv created 2017/03/10 · arxiv updated 2017/03/13 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/28

Abstract

It is proved that Epstein's zeta-function ζ_Q(s), related to a positive definite integral binary quadratic form, has a zero 1/2 + iγ with T ≤ γ≤ T + T^3/7 +ε 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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