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


Journal Article

© 2018 London Mathematical Society Under the Riemann Hypothesis, we prove for any natural number r there exist infinitely many natural numbers n such that (γn+r-γn/(2πr/log γn) >+Θ/r and (γn+r-γn/(2πr/log γn)<1-v for explicit absolute positive constants Θ and v, 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.

Full Text

Cited Authors

  • Conrey, JB; Turnage-Butterbaugh, CL

Published Date

  • April 1, 2018

Published In

Volume / Issue

  • 50 / 2

Start / End Page

  • 349 - 356

Electronic International Standard Serial Number (EISSN)

  • 1469-2120

International Standard Serial Number (ISSN)

  • 0024-6093

Digital Object Identifier (DOI)

  • 10.1112/blms.12142

Citation Source

  • Scopus