Small gaps between consecutive zeros of the Riemann zeta-function

TL;DR

This paper introduces a new resonance-correlation method combining existing approaches to analyze small gaps between zeros of the Riemann zeta-function, achieving improved bounds under the Riemann Hypothesis.

Contribution

The paper presents a novel synthesis of pair correlation and Montgomery-Odlyzko methods to better estimate small gaps between zeros of the zeta-function.

Findings

Proves that the normalized gap .50895 under RH

Breaks previous practical barrier around 0.515

Introduces the resonance-correlation method for zero gap analysis

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 $\mu < 0.50895$ under the Riemann Hypothesis.