On Congruences with Products of Variables from Short Intervals and Applications
Number Theory
2012-03-02 v1
Abstract
We obtain upper bounds on the number of solutions to congruences of the type modulo a prime with variables from some short intervals. We give some applications of our results and in particular improve several recent estimates of J. Cilleruelo and M. Z. Garaev on exponential congruences and on cardinalities of products of short intervals, some double character sum estimates of J. B. Friedlander and H. Iwaniec and some results of M.-C. Chang and A. A. Karatsuba on character sums twisted with the divisor function.
Keywords
Cite
@article{arxiv.1203.0017,
title = {On Congruences with Products of Variables from Short Intervals and Applications},
author = {Jean Bourgain and Moubariz Garaev and Sergei Konyagin and Igor Shparlinski},
journal= {arXiv preprint arXiv:1203.0017},
year = {2012}
}