Asymptotic behavior "almost everywhere" of additive and multiplicative arithmetic functions

TL;DR

This paper investigates the 'almost everywhere' asymptotic behavior of additive and multiplicative arithmetic functions, identifying classes where their asymptotics align with strongly additive and multiplicative functions, supported by proofs and examples.

Contribution

It introduces classes of arithmetic functions with asymptotics that coincide 'almost everywhere' with their strongly additive or multiplicative counterparts.

Findings

Identified classes where asymptotics coincide 'almost everywhere'

Proved several assertions regarding these classes

Provided illustrative examples

Abstract

We define the asymptotic behavior "almost everywhere" of additive and multiplicative arithmetic functions in the paper. Classes of additive and multiplicative arithmetic functions are singled out for which the asymptotics coincides "almost everywhere" with the asymptotics of the corresponding strongly additive and multiplicative arithmetic functions. Several assertions are proved and examples are considered.