DYNAMICAL SYSTEMS ON ARITHMETIC FUNCTIONS DETERMINED BY PRIMES

In this paper, we study an algebra A consisting of all arithmetic functions, and corresponding dynamical systems acting on A determined by a fixed prime p. Starting from free probabilistic models on A determined by p, we construct certain group dynamical systems induced by the additive group R of all real numbers. We investigate the basic properties and free-probabilistic data of such dynamical systems by constructing corresponding crossed product algebras.