On the use of the method of moments for the study of additive functions (Q1179502)

The typical tools for the proof of a limiting law for additive functions are the sieve methods (Kubilius model) or characteristic functions and Dirichlet series. In the case of the classical Erdős-Kac theorem, an alternative proof by the method of moments was given by \textit{H. Halberstam} [J. Lond. Math. Soc. 30, 43--53 (1955; Zbl 0064.04202)]. In this paper the method of moments is extended to work for a wide class of problems, including a theorem of Erdős on limiting distribution with centering but without norming, and a theorem of Kubilius. Two important ideas are (i) a truncation, so that the methods work even where moments of the function do not converge, and (ii) the application of moments to calculate the characteristic function via a power-series expansion.