Work

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

Year: 2018

Type: article

Abstract: Under the Riemann Hypothesis, we prove for any natural number r there exist infinitely many natural numbers n such that ( γ n + r − γ n ) / ( 2 π r / log γ n ) > 1 + Θ / r and ( γ n + r − γ n ) / ( 2 π r / log γ n ) < 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.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.12142

Authors: J. Brian Conrey, Caroline L. Turnage‐Butterbaugh

Institutions: American Institute of Mathematics, University of Bristol, Duke University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Mathematical Sciences Research Institute (MSRI)