Asymptotic of summation arithmetic functions, the limit for which is the law of normal distribution

TL;DR

This paper investigates summation arithmetic functions with asymptotically independent terms and proves their convergence to the normal distribution, providing insights into their asymptotic behavior.

Contribution

It establishes the asymptotic normality of summation arithmetic functions with asymptotically independent terms, advancing understanding of their limiting distribution.

Findings

Proved the limit law for summation arithmetic functions is the normal distribution.

Established conditions for asymptotic independence in these functions.

Demonstrated the asymptotic behavior through rigorous proofs.

Abstract

Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.