Non-Standard Limit Theorems in Number Theory

TL;DR

This paper introduces a limit theorem for a probabilistic model of square-free numbers, revealing a limiting distribution derived from the Dickman-De Bruijn function with constant density on [0,1], and provides error estimates.

Contribution

It presents a novel limit theorem describing the distribution of square-free numbers using the Dickman-De Bruijn function, including error term estimates.

Findings

Limiting distribution has a density from the Dickman-De Bruijn function.

Density is constant on the interval [0,1].

Provides estimates for the error term in the limit theorem.

Abstract

We present a limit theorem describing the behavior of a probabilistic model for square-free numbers. The limiting distribution has a density that comes from the Dickman-De Bruijn function and is constant on the interval $[0,1]$. We also provide estimates concerning the error term in the limit theorem.