J. Aust. Math. Soc.  81 (2006), 425-440
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
and
G. Stepanauskas
  Department of Mathematical Informatics
  Vilnius University
  Naugarduko 24
  03225 Vilnius
  Lithuania
  gediminas.stepanauskas@maf.vu.lt


Abstract
We consider the weak convergence of the set of strongly additive functions $f(q)$ with rational argument $q$. It is assumed that $f(p)$ and $f(1/p)\in\{0,1\}$ 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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