Modular hyperbolas and bilinear forms of Kloosterman sums

Abstract

In this paper we study incidences for hyperbolas in ${\mathbf{F}}_p$ and show how linear sum--product methods work for such curves. As an application we give a purely combinatorial proof of a nontrivial upper bound for bilinear forms of Kloosterman sums.

arXiv comment27 pages