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
SN - 0024-6093
VL - 50
SP - 349
EP - 356
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
IS - 2
ER -