A point-line incidence identity in finite fields, and applications

Abstract

Let $E\subseteq {\mathbb{F}}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements. We prove an identity for the second moment of its incidence function and deduce a variety of existing results from the literature, not all naturally associated with lines in ${\mathbb{F}}_q^2$, in a unified and elementary way.

30 pages

References in corpus (1)

• Growth Estimates in Positive Characteristic via Collisions

Cited by in corpus (3)

• New results on sum-product type growth over fields
• On the Pinned Distances Problem in Positive Characteristic
• Products of Differences in Prime Order Finite Fields