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

J. Brian Conrey; Caroline L. Turnage-Butterbaugh

doi:10.1112/blms.12142

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

J. Brian Conrey, Caroline L. Turnage-Butterbaugh

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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
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	https://doi.org/10.1112/blms.12142
Publication status	Published - Apr 2018

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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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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/85041043094

UR - https://arxiv.org/abs/1708.00030

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ER -

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

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