On a variance for twins of $k-$free numbers in arithmetic progressions

TL;DR

This paper establishes a new upper bound for the variance of twin $k$-free numbers in arithmetic progressions, extending understanding of their distribution.

Contribution

It introduces a novel upper bound of Barban-Davenport-Halberstam type specifically for twins of $k$-free numbers in arithmetic progressions.

Findings

New upper bound for variance of twin $k$-free numbers

Extension of distribution results in arithmetic progressions

Improved understanding of twin $k$-free number patterns

Abstract

In this paper, we give a new upper bound of Barban-Davenport-Halberstam type for twins of $k-$free numbers in arithmetic progressions.