The joint limit theorem for distributions of integer valued additive functions

Author:

ŠIAULYS Jonas

AMS Classification:

11K65

Keywords:

additive functions, frequency, logarithmic frequency, weak convergence

Abstract:

The necessary and sufficient conditions for the weak convergence of \nu_x(n\leqslant x, f_x(n)<u) and \mu_x(n\leqslant x, f_x(n)<u) to the same limit law are obtained. Here \nu_x(n\leqslant x, f_x(n)<u) is the distribution of a set of strongly additive functions f_x with respect to the usual frequency on the positive integers, and \mu_x(n\leqslant x, f_x(n)<u) is the distribution of the same set with respect to the logarithmic frequency. The case when f_x(p)\in \{0,1\} for every prime p is considered.

Download paper:

Siaulys-06.pdf

Vol. 1 (9), 2006