Distributions of differences of Riemann zeta zeros

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.