A modular Szemerédi-Trotter theorem for hyperbolas (Q1759772)

Let \(P\) be a finite set of points and let \(L\) be a finite set of lines. The Szemerédi-Trotter theorem gives an upper estimation to the number of incidences between \(P\) and \(L\). In this paper the author proves a Szemerédi-Trotter type theorem for hyperbolas in \(\mathbb{F}_{p} \times \mathbb{F}_{p}\). The proof is based on the expansion properties in \(\text{SL}_{2}(\mathbb{F}_{p})\).