On Bourgain's bound for short exponential sums and squarefree numbers

TL;DR

This paper leverages Bourgain's recent bounds on short exponential sums to establish new independence results concerning the distribution of squarefree numbers within arithmetic progressions.

Contribution

It introduces novel applications of Bourgain's bounds to analyze the distribution of squarefree numbers in arithmetic progressions.

Findings

Proves independence results for squarefree numbers in arithmetic progressions.

Demonstrates the effectiveness of Bourgain's bounds in number theory.

Provides new insights into the distribution patterns of squarefree integers.

Abstract

We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.