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

2021/06/03 by Victor Volfson, Volfson, Victor
Mathematics · #11K65 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2106.10237

openalex publication_date 2021/06/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

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.

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