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/