Kloosterman sums in residue rings

J. Bourgain, and M. Z. Garaev. "Kloosterman sums in residue rings." Acta Arithmetica 164.1 (2014): 43-64. <http://eudml.org/doc/279415>.

@article{J2014,
abstract = {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.},
author = {J. Bourgain, M. Z. Garaev},
journal = {Acta Arithmetica},
keywords = {Kloosterman sums; multilinear exponential sums; general modulus; congruences},
language = {eng},
number = {1},
pages = {43-64},
title = {Kloosterman sums in residue rings},
url = {http://eudml.org/doc/279415},
volume = {164},
year = {2014},
}

TY - JOUR
AU - J. Bourgain
AU - M. Z. Garaev
TI - Kloosterman sums in residue rings
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 1
SP - 43
EP - 64
AB - 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.
LA - eng
KW - Kloosterman sums; multilinear exponential sums; general modulus; congruences
UR - http://eudml.org/doc/279415
ER -