\'Etude statistique du facteur premier m\'edian, 3 : lois de r\'epartition

TL;DR

This paper investigates the distribution of the middle prime factor of integers, establishing a Gaussian limit law and providing an optimal convergence rate, thus advancing the understanding of prime factorization statistics.

Contribution

It introduces an improved bound on the convergence speed to the Gaussian law for the middle prime factor distribution, refining previous results.

Findings

Established a Gaussian limit law for the middle prime factor

Derived an optimal bound for the convergence rate

Enhanced previous estimates in the literature

Abstract

We consider the Gaussian limit law for the distribution of the middle prime factor of an integer, defined according to multiplicity or not. We obtain an optimal bound for the speed of convergence, thereby improving on previous estimates available in the literature.