English

On the distribution of squarefree integers in arithmetic progressions

Number Theory 2014-11-11 v1

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 (Z/qZ)×(\mathbb{Z}/q\mathbb{Z})^{\times} which considerably improves upon earlier work of Blomer.

Keywords

Cite

@article{arxiv.1411.2360,
  title  = {On the distribution of squarefree integers in arithmetic progressions},
  author = {Pierre Le Boudec},
  journal= {arXiv preprint arXiv:1411.2360},
  year   = {2014}
}