The Riemann zeta distribution

Let zeta be the Riemann zeta function. Khinchine (1938) proved that the fun ction f(sigma)(t) = zeta(sigma + it)/zeta(sigma), where sigma > 1 and t is real, is an infinitely divisible characteristic function. We investigate fu rther the fundamental proper-ties of the corresponding distribution of f(si gma), the Riemann zeta distribution, including its support and unimodality. In particular, the Riemann zeta random variable is represented as a linear function of infinitely many independent geometric random variables. To ext end Khinchine's result, we construct the Dirichlet-type characteristic func tions of discrete distributions and provide a sufficient condition for the infinite divisibility of these characteristic functions. By way of applicat ions, we give probabilistic proofs for some identities in number theory, in cluding a new identity for the reciprocal of the Riemann zeta function.