Delange's Tauberian theorem and asymptotic normality of random ordered factorizations of integers

TL;DR

This paper demonstrates that the number of factors in random ordered factorizations of integers follows an asymptotic normal distribution, using Dirichlet series and Delange's Tauberian theorems.

Contribution

It introduces a novel approach combining Dirichlet series and Tauberian theorems to establish asymptotic normality in integer factorizations.

Findings

Number of factors is asymptotically normally distributed

Uses Dirichlet series and Tauberian theorems for proof

Provides a new probabilistic understanding of integer factorizations

Abstract

By a suitable shifting-the-mean parametrization at the Dirichlet series level and Delange's Tauberian theorems, we show that the number of factors in random ordered factorizations of integers is asymptotically normally distributed.