J. Aust. Math. Soc.
81 (2006), 425440

The factorial moments of additive functions with rational argument

J. Siaulys
Department of Probability
Theory and Number Theory
Vilnius University
Naugarduko 24
03225 Vilnius
Lithuania
jonas.siaulys@mif.vu.lt





Abstract

We consider the weak convergence of the set of
strongly additive functions with rational argument
. It is assumed that
and for all primes. We obtain necessary and
sufficient conditions of the convergence to the
limit distribution. The proof is based on the
method of factorial moments. Sieve results, and
Halász's and Ruzsa's inequalities are
used. We present a few examples of application of
the given results to some sets of fractions.

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