On the distribution of squarefree integers in arithmetic progressions

Abstract

We investigate the error term of the asymptotic formula for the number of squarefree integers up to some bound, and lying in some arithmetic progression a (mod q). In particular, we prove an upper bound for its variance as a varies over $(\mathbb{Z}/q\mathbb{Z}{)}^{\times }$ which considerably improves upon earlier work of Blomer.