Some limit laws for strongly additive prime indicators

Authors:

Jonas ŠIAULYS, Gediminas STEPANAUSKAS

AMS Classification:

11K65

Keywords:

additive function, binomial distribution, frequency, limit law, Poisson distribution, weak convergence

Abstract:

Some examples of weak limit laws for distributions \nu_x( f_x(n)<u)=\frac{1}{[x]}\sum\limits_{\substack{n\leqslant x\\ f_x(n)<u}}1 are presented, where f_x is a set of strongly additive functions. The case when f_x(p)\in \{0,1\} for every prime p is considered. As limit laws there are investigated the Poisson, Bernoulli, binomial, geometrical distributions and some mixtures of them.

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siaulys-stepanauskas-08.pdf

Vol. 3 (11), 2008