# Asymptotics of the $k$-free diffraction measure via discretisation

## TL;DR

This paper investigates the diffraction pattern of $k$-free integers, providing asymptotic analysis of the diffraction measure close to the origin, which enhances understanding of their spectral properties.

## Contribution

It introduces a novel asymptotic analysis of the $k$-free diffraction measure using discretisation techniques, advancing the mathematical understanding of these structures.

## Key findings

- Derived the asymptotic behavior of the diffraction measure near zero
- Established new discretisation methods for analyzing $k$-free integers
- Enhanced spectral understanding of $k$-free integer sets

## Abstract

We determine the diffraction intensity of the $k$-free integers near the origin.