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

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)349-356
Number of pages8
JournalBulletin of the London Mathematical Society
Volume50
Issue number2
Early online date29 Jan 2018
DOIs
DateAccepted/In press - 18 Nov 2017
DateE-pub ahead of print - 29 Jan 2018
DatePublished (current) - Apr 2018

Abstract

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.

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    Rights statement: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Wiley at https://doi.org/10.1112/blms.12142 . Please refer to any applicable terms of use of the publisher.

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