Statistics on Riemann zeros

2011/12/01 by Marco, Ricardo Perez · 1 citation
#11M26 #Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1112.0346

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.

Cited by

• Generalization of the Ford-Zaharescu Theorem

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