One limit theorem for distributions of additive functions

Author:

ŠIAULYS Jonas

AMS Classification:

11K65

Keywords:

additive functions, frequency, Poisson law, weak convergence

Abstract:

The criteria for the weak convergence of \nu^\alpha_x( f_x(n)<u) to the Poisson limit law is obtained. Here \nu^\alpha_x( f_x(n)<u) denote the distribution function of a set of strongly additive functions f_x with respect to the frequency \nu^\alpha_x(\mathcal{A}_x)=\bigg\{\sum\limits_{m\leqslant x}\frac1{m^\alpha}\bigg\}^{-1}\sum\limits_{\substack{m\leqslant x\\ m\in\mathcal{A}_x}}\frac1{m^\alpha}, \quad \alpha\in[0,1]. The case when f_x(p)\in \{0,1\} for every prime p is considered.

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Siaulys-07-pdf.pdf

Vol. 2 (10), 2007