Characterization of riemann zeta distribution

Abstract

The characterization of Riemann Zeta distribution is presented based on its characteristic function properties, where the characteristic function of Riemann Zeta distribution is obtained by using Fourier-Stieltjes transform to be a normalized Zeta function. The characteristic function property is exposed to be in the quadratic form as definite non-negative function property. The combination of this property and its continuity provided infinite divisibility of Riemann Zeta distribution where this characteristic function is also obtained as the characteristic function from compound Poisson distribution.