On some results in probabilistic number theory (Q1969263)

This expository article surveys some problems and results in probabilistic number theory, an area to which the author has made many contributions. Although there are no proofs, some indication of the general methods used are given. The author concentrates on distribution functions associated with some types of strongly additive functions \(f\). He quotes ten theorems covering a representative collection of results in the literature. Most of these are concerned with giving necessary and sufficient conditions, or just sufficient conditions, in order that the frequency \(n^{-1} \#\{m\leq n : f(m) < C_n +D_n x\}\) converges weakly to a distribution function. In some cases an estimate of the rate of convergence or further terms in the asymptotic expansion are given.