An analog of the Furstenberg-Katznelson-Weiss theorem on triangles in sets of positive density in finite field geometries

Abstract

We prove that if the cardinality of a subset of the 2-dimensional vector space over a finite field with $q$ elements is $\ge \rho q^2$, with $\frac{1}{\sqrt{q}}<<\rho \le 1$, then it contains an isometric copy of $\ge c\rho q^3$ triangles.

Cited by in corpus (2)

• The number of occurrences of a fixed spread among n directions in vector spaces over finite fields
• On the solvability of systems of bilinear equations in finite fields