Moments of the distribution of $k$-free numbers in short intervals and arithmetic progressions

TL;DR

This paper investigates the distribution of k-free numbers within short intervals and arithmetic progressions, providing estimates that align with Montgomery's conjecture in specific ranges.

Contribution

It offers new estimates for the distribution of k-free numbers in short intervals and progressions, supporting Montgomery's conjecture in certain cases.

Findings

Estimates for k-free numbers distribution in short intervals

Results consistent with Montgomery's conjecture in specific ranges

Enhanced understanding of number distribution patterns

Abstract

We show estimates for the distribution of $k$-free numbers in short intervals and arithmetic progressions. We argue that, at least in certain ranges, these estimates agree with a conjecture by H. L. Montgomery.