Small gaps between consecutive zeros of the Riemann zeta-function

Abstract

In this paper, we introduce the resonance-correlation method to study small gaps between consecutive zeros of the Riemann zeta-function. Our method is based on a synthesis of Montgomery's pair correlation approach and the Montgomery-Odlyzko method. As an application, we break the persistent practical barrier around $0.515$ and prove $\hat{I}¼<0.50895$ under the Riemann Hypothesis.

14 pages