Geodesic
Integral Limit Laws for Additive Functions
Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 194-203

Voir la notice de l'article provenant de la source Cambridge University Press

In the present paper a general form of integral limit laws for additive functions is obtained. Our limit law contains Kubilius’ results [5] on his class H. In the proof we make use of characteristic functions (Fourier transforms), which reduces our problem to finding asymptotic formulas for sums of multiplicative functions. This requires an extension of previous results in order to enable us to take into consideration the parameter of the characteristic function in question. We call this extension a parametric mean value theorem for multiplicative functions and its proof is analytic on the line of [4]. 
Galambos, J. Integral Limit Laws for Additive Functions. Canadian journal of mathematics, Tome 25 (1973) no. 1, pp. 194-203. doi: 10.4153/CJM-1973-017-3
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