Statistics on Riemann zeros

Abstract

We numerically study the statistical properties of differences of zeros of Riemann zeta function and L-functions predicted by the theory of the eñe product. In particular, this provides a simple algorithm that computes any non-real Riemann zeros from very large ones ("self-replicating property of Riemann zeros"). Also the algorithm computes the full sequence of non-real zeros of Riemann zeta function from the sequence of non-real zeros of any Dirichlet L-function ("zeros of L-functions know about Riemann zeros"). We also check that the first error to the convergence to the classical GUE statistic near 0 is a Fresnel distribution.

47 pages, 75 figures

Cited by in corpus (8)

• Notes on the Riemann Hypothesis
• Some sums over the non-trivial zeros of the Riemann zeta function
• The eñe product over a commutative ring
• Distributions of differences of Riemann zeta zeros
• On the statistics of differences of zeta zeros starting from zero number $10^{23}$
• On the self-replicating properties of Riemann zeta zeros: A statistical study
• The Mangoldt function and the non-trivial zeros of the Riemann zeta function
• On Statistics of the Riemann Zeros Differences