On two conjectures concerning squarefree numbers in arithmetic progressions
Number Theory
2015-12-14 v1
Abstract
We prove upper bounds for the error term of the distribution of squarefree numbers up to in arithmetic progressions modulo 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 M\"obius function by Bourgain and Fouvry-Kowalski-Michel.
Keywords
Cite
@article{arxiv.1512.03648,
title = {On two conjectures concerning squarefree numbers in arithmetic progressions},
author = {Ramon M. Nunes},
journal= {arXiv preprint arXiv:1512.03648},
year = {2015}
}
Comments
18 pages, no figures; comments are welcome