Asymptotics of probability characteristics of additive arithmetic functions

TL;DR

This paper investigates the asymptotic behavior of probabilistic characteristics of additive arithmetic functions, providing new estimations regardless of the existence of a limit distribution, and compares different classes of such functions.

Contribution

It introduces new asymptotic estimations for probabilistic characteristics of additive functions, including those without a limit distribution, and compares classes with similar asymptotic behaviors.

Findings

Established asymptotic estimations for strongly additive functions

Extended results to functions with similar probabilistic characteristics

Provided bounds regardless of limit distribution existence

Abstract

We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the estimation of the asymptotics of the probabilistic characteristics of strongly additive arithmetic functions, as well as additive functions of the class that have the same asymptotic behavior of the probabilistic characteristics, as for strongly additive arithmetic functions.