The proof of the existence of a limit distribution for arithmetic multiplicative functions with values in the interval $\lbrack-1, 1\rbrack$, and characterizations of degenerateness and symmetry for such a distribution, can be obtained in a simple manner by combining the famous mean-value theorem of Wirsing with the method of moments of probability theory.
Publié le : 1990-04-14
Classification:
Multiplicative function,
limit distribution,
mean value,
method of moments,
11N64,
60F05
@article{1176990866,
author = {de la Cal, Jesus},
title = {On the Limit Distribution of Multiplicative Functions with Values in the Interval $\lbrack -1, 1 \rbrack$},
journal = {Ann. Probab.},
volume = {18},
number = {4},
year = {1990},
pages = { 901-904},
language = {en},
url = {http://dml.mathdoc.fr/item/1176990866}
}
de la Cal, Jesus. On the Limit Distribution of Multiplicative Functions with Values in the Interval $\lbrack -1, 1 \rbrack$. Ann. Probab., Tome 18 (1990) no. 4, pp. 901-904. http://gdmltest.u-ga.fr/item/1176990866/