Convergence to the Poisson law. III: Method of moments (Q1567894)

The author generalizes his previous results concerning the convergence of the distribution of strongly additive arithmetic functions with integer values to the Poisson law. His main result states, using the values of such functions at prime numbers, a necessary and sufficient condition for the convergence of distribution to the Poisson law is given. Proofs are based on the method of moments giving the possibility of studying this arithmetic function without other conditions. Part II, cf. Lith. Math. J. 36, No. 3, 314--322 (1996); translation from Liet. Mat. Rink. 36, No. 3, 393--404 (1996; Zbl 0886.11050).