On two conjectures concerning squarefree numbers in arithmetic progressions

Abstract

We prove upper bounds for the error term of the distribution of squarefree numbers up to $X$ in arithmetic progressions modulo $q$ making progress towards two well-known conjectures concerning this distribution and improving upon earlier results by Hooley. We make use of recent estimates for short exponential sums by Bourgain-Garaev and for exponential sums twisted by the Möbius function by Bourgain and Fouvry-Kowalski-Michel.

arXiv comment18 pages, no figures; comments are welcome

References in corpus (1)

• On the distribution of squarefree integers in arithmetic progressions

Cited by in corpus (1)

• Squarefree integers in large arithmetic progressions