A variance for $k$-free numbers in arithmetic progressions of given modulus

TL;DR

This paper improves the error term in the asymptotic formula for the variance of squarefree numbers in arithmetic progressions with a fixed modulus, refining previous results by Nunes.

Contribution

It provides an improved error estimate in the asymptotic formula for the variance of k-free numbers in arithmetic progressions.

Findings

Enhanced accuracy in variance estimation for squarefree numbers

Refined error bounds in asymptotic formulas

Improved understanding of distribution of k-free numbers

Abstract

An asymptotic formula for the variance of squarefree numbers in arithmetic progressions of given modulus was obtained by Nunes (see reference [3]). We improve one of the error terms.