Skip to content

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
Issue number2
Early online date29 Jan 2018
DateAccepted/In press - 18 Nov 2017
DateE-pub ahead of print - 29 Jan 2018
DatePublished (current) - Apr 2018


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.

Download statistics

No data available



  • Full-text PDF (accepted author manuscript)

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

    Accepted author manuscript, 148 KB, PDF document

    Licence: Other


View research connections

Related faculties, schools or groups