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

摘要

Under the Riemann Hypothesis, we prove for any natural number r there exist infinitely many natural numbers n such that (n+r-n)/(2r/logn)1+/for explicit absolute positive constants and ?, where 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.