### 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.

Original language | English |
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Pages (from-to) | 349-356 |

Number of pages | 8 |

Journal | Bulletin of the London Mathematical Society |

Volume | 50 |

Issue number | 2 |

Early online date | 29 Jan 2018 |

DOIs | |

Publication status | Published - Apr 2018 |

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## Cite this

Conrey, J. B., & Turnage-Butterbaugh, C. L. (2018). On r-gaps between zeros of the Riemann zeta-function.

*Bulletin of the London Mathematical Society*,*50*(2), 349-356. https://doi.org/10.1112/blms.12142