A small improvement in the gaps between consecutive zeros of the Riemann zeta-function

Feng and Wu introduced a new general coefficient sequence into Montgomery and Odlyzko’s method for exhibiting irregularity in the gaps between consecutive zeros of ζ(s) assuming the Riemann hypothesis. They used a special case of their sequence to improve upon earlier results on the gaps. In this paper we consider a general sequence related to that of Feng and Wu, and introduce a somewhat less general sequence { an} for which we write the Montgomery–Odlyzko expressions explicitly. As an application, we give the following slight improvement of Feng and Wu’s result: infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at most 0.515396 times the average spacing and infinitely often they differ by at least 2.7328 times the average spacing. © 2016, The Author(s).