Small gaps and small spacings between zeta zeros

TL;DR

Under the assumption of the Riemann Hypothesis, this paper demonstrates that phenomena related to pairs of zeta zeros occur with positive density, and it examines the differences between distinct zeros rather than double zeros.

Contribution

It extends the understanding of zero pair correlations by showing their positive density and clarifies the distinction between double zeros and close pairs.

Findings

Pair correlation phenomena occur with positive density under RH.

Differences between distinct zeros are analyzed separately from double zeros.

Provides insights into the distribution and spacing of zeta zeros.

Abstract

We show assuming RH that phenomena concerning pairs of zeros established $via$ pair correlations occur with positive density (with at most a slight adjustment of the constants). Also, while a double zero is commonly considered to be a close pair, we consider the difference between two $distinct$ zeros.