Distributions of differences of Riemann zeta zeros

TL;DR

This paper investigates the statistical properties of differences between Riemann zeta zeros at large, revealing consistent distribution patterns, skewness towards zeros, and the ability to fit these distributions with Johnson PDFs.

Contribution

It provides a detailed analysis of the distributional characteristics of zeta zero differences and demonstrates their fit with Johnson probability density functions.

Findings

Differences of zeta zeros have similar statistical properties regardless of their location.

Distributions are skewed towards the nearest zero and exhibit local maxima of variance.

Distributions can be effectively modeled using Johnson PDFs.

Abstract

We study distributions of differences of unscaled Riemann zeta zeros, $\gamma-\gamma'$, at large. We show, that independently of the location of the zeros, their differences have similar statistical properties. The distributions of differences are skewed towards the nearest zeta zero, have local maximum of variance and local minimum of kurtosis at or near each zeta zero. Furthermore, we show that distributions can be fitted with Johnson probability density function, despite the value of skewness or kurtosis of the distribution.