Additive arithmetic functions with limit normal distribution

TL;DR

This paper establishes conditions under which additive arithmetic functions converge to a normal distribution, generalizes the Erdos-Kac theorem, and analyzes the rate of convergence with practical examples.

Contribution

It provides new sufficient conditions for normal convergence of additive functions and extends the Erdos-Kac theorem with convergence rate analysis.

Findings

Generalized the Erdos-Kac theorem

Established sufficient conditions for normal convergence

Provided examples illustrating the assertions

Abstract

This paper proves several assertions on sufficient conditions for the convergence of additive arithmetic functions to the normal distribution. A generalization of the Erdos-Kac theorem was proved and determines the rate of convergence of additive arithmetic functions to the normal distribution in the cases considered. The paper provides examples of using the proved assertions.