Sieving and the Erd{\H o}s-Kac theorem

TL;DR

This paper presents an accessible proof of the Erdős-Kac theorem using moment calculations, extending it within sieve theory and connecting to related results in number theory.

Contribution

It introduces a simplified proof method for the Erdős-Kac theorem and demonstrates its extension in sieve theory, linking to existing literature.

Findings

Proof of Erdős-Kac theorem via moments

Extension of proof within sieve theory

Connections to related number theory results

Abstract

We give a relatively easy proof of the Erd\H os-Kac theorem via computing moments. We show how this proof extends naturally in a sieve theory context, and how it leads to several related results in the literature.