On large gaps between zeros of the Riemann zeta-function

TL;DR

Under the assumption of the Generalized Riemann Hypothesis, the paper proves that there are infinitely many pairs of consecutive zeros of the Riemann zeta-function separated by at least 3.072 times the average gap, highlighting large zero gaps.

Contribution

The paper establishes a new lower bound on the size of large gaps between consecutive zeros of the Riemann zeta-function assuming GRH.

Findings

Infinitely many large gaps between zeros exist under GRH.

Large gaps are at least 3.072 times the average spacing.

Supports the understanding of zero distribution in analytic number theory.

Abstract

Assuming the Generalized Riemann Hypothesis(GRH), we show that infinitely often consecutive non-trivial zeros of the Riemann zeta-function differ by at least 3.072 times the average spacing.