On r-gaps between zeros of the Riemann zeta-function

J. Brian Conrey, Caroline L. Turnage-Butterbaugh

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Under the Riemann Hypothesis, we prove for any natural number r there exist infinitely many natural numbers n such that (γn+r-γn)/(2πr/logγn)>1+Θ/r and (γn+r-γn)/(2πr/logγn)<1-θ/r for explicit absolute positive constants Θ and θ, where γ denotes an ordinate of a zero of the Riemann zeta-function on the critical line. Selberg published announcements of this result several times without proof.

Original languageEnglish
Pages (from-to)349-356
Number of pages8
JournalBulletin of the London Mathematical Society
Issue number2
Early online date29 Jan 2018
Publication statusPublished - Apr 2018

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