On properties of the Riemann zeta distribution
On properties of the Riemann zeta distribution
We examine various properties of positive integers selected according to the Riemann zeta distribution. That is, if ζ(s)=∑n≥11∕ns, s>1, then we consider the random variable Xs with P(Xs=n)=1∕(ζ(s)ns), n≥1. We derive various results such as the analog of the Erdös–Kac central limit theorem (CLT) for the number of distinct prime …