# On the proximity of multiplicative functions to the function counting prime factors with multiplicity

## TL;DR

This paper investigates the similarity between multiplicative functions and additive functions, providing bounds on the number of integers where they agree, thus advancing understanding of their structural relationship.

## Contribution

It establishes a lower bound for the count of integers where a multiplicative function matches a given additive function, highlighting their proximity.

## Key findings

- Lower bound for E(Ω,g,x) established
- Quantitative measure of similarity between multiplicative and additive functions
- Insights into the structural relationship between these classes of functions

## Abstract

We examine how closely a multiplicative function resembles an additive function. Given a multiplicative function $g$ and an additive function $f$, we examine the size of the quantity $E(f,g;x)=\# \{n\leq x:f(n)=g(n)\}$. We establish a lower bound for $E(\Omega,g,x)$.