# Scaling of the diffraction measure of $k$-free integers near the origin

## TL;DR

This paper derives asymptotic formulas for how the diffraction intensity of $k$-free integers scales near the origin, providing insights into the structure and fluctuations of these number sets.

## Contribution

It introduces new asymptotic results for the diffraction measure of $k$-free integers, advancing understanding of their local fluctuation behavior.

## Key findings

- Derived asymptotics for diffraction intensity near the origin.
- Quantified the degree of patch fluctuations in $k$-free integers.
- Enhanced the mathematical understanding of the structure of $k$-free integers.

## Abstract

Asymptotics are derived for the scaling of the total diffraction intensity for the set of $k$-free integers near the origin, which is a measure for the degree of patch fluctuations.