TY - JOUR

T1 - On r-gaps between zeros of the Riemann zeta-function

AU - Conrey, J. Brian

AU - Turnage-Butterbaugh, Caroline L.

PY - 2018/4

Y1 - 2018/4

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 - http://www.scopus.com/inward/record.url?scp=85041043094&partnerID=8YFLogxK

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

U2 - 10.1112/blms.12142

DO - 10.1112/blms.12142

M3 - Article (Academic Journal)

AN - SCOPUS:85041043094

VL - 50

SP - 349

EP - 356

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

SN - 0024-6093

IS - 2

ER -