Title: “The Riemann zeta distribution.”

Abstract: We examine statistical properties of integers when they are sampled using the Riemann zeta distribution and compare to similar properties when they are sampled according to “uniform” or harmonic distributions.  For example, as the variable in the Riemann zeta function approaches 1, a central limit theorem and large and moderate deviations for the distinct number of prime factors for the sampled integer can be readily derived. These results can then be deduced for the uniform distribution via a Tauberian Theorem.