We generalize some of our previous results on Kloosterman sums [Izv. Mat., to appear] for prime moduli to general moduli. This requires establishing the corresponding additive properties of the reciprocal-set I¯¹ = {x¯¹: x ∈ I}, where I is an interval in the ring of residue classes modulo a large positive integer. We apply our bounds on multilinear exponential sums to the Brun-Titchmarsh theorem and the estimate of very short Kloosterman sums, hence generalizing our earlier work to the setting of general moduli.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-1-4,
author = {J. Bourgain and M. Z. Garaev},
title = {Kloosterman sums in residue rings},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {43-64},
zbl = {1319.11051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-1-4}
}
J. Bourgain; M. Z. Garaev. Kloosterman sums in residue rings. Acta Arithmetica, Tome 166 (2014) pp. 43-64. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-1-4/