An estimate of asymptotics of the moments of additive arithmetic functions with a limit distribution defined on a subset of the natural series

TL;DR

This paper investigates the asymptotic behavior of moments of additive arithmetic functions with a limit distribution, extending results to functions defined on subsets of natural numbers and arithmetic progressions.

Contribution

It provides new asymptotic estimates for moments of strongly additive functions and functions in class H with limit distributions on specific subsets.

Findings

Derived asymptotic formulas for moments of additive functions

Extended analysis to functions on arithmetic progressions

Established conditions for limit distribution-based asymptotics

Abstract

We study the asymptotics of the moments of arithmetic functions that have a limit distribution, not necessarily normal, defined on a subset of the natural series that satisfies certain requirements. Several assertions are proved on estimating the asymptotics of the moments of strongly additive arithmetic functions and also with additive functions of the class H that have a limit distribution and are defined on a subset of the natural series. The first version of the article is devoted to the study of the asymptotics of the moments of arithmetic functions that have a limit distribution on the natural series. The second version of the article is devoted to the study of the asymptotics of the moments of arithmetic functions that have a limit distribution on an arithmetic progression.