The convergence to the Poisson law. II: Unbounded strongly additive functions (Q1366367)

In the first part [ibid. 35, 300-308 (1995; Zbl 0865.11056)], the convergence of a sequence of additive functions to a Poisson law was described under some conditions, which the reviewer felt were unnecessary. Here they are indeed removed, at least if the functions are assumed to be strongly additive; the only remaining assumption is the natural one that \( \sum _{\sqrt p<x\leq x,\;f_x(p)\neq 0} 1/p \rightarrow 0\).