We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa7896-12-2015,
author = {Ramon M. Nunes},
title = {On Bourgain's bound for short exponential sums and squarefree numbers},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {99-116},
zbl = {06545342},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa7896-12-2015}
}
Ramon M. Nunes. On Bourgain's bound for short exponential sums and squarefree numbers. Acta Arithmetica, Tome 172 (2016) pp. 99-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa7896-12-2015/