Distributions of differences of Riemann zeta zeros

2020/01/12 by J. Takalo, Takalo, Jouni Juhani · 1 citation
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #11Z05 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #G.3 #Number Theory (math.NT) #Other Statistics (stat.OT) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2001.05294

openalex publication_date 2020/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study distributions of differences of unscaled Riemann zeta zeros, γ-γ', 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.

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