On the Number of Dot Products Determined by a Large Set and One of its Translates in Finite Fields

Abstract

Let $E\subseteq {\mathbb{F}}_q^2$ be a set in the 2-dimensional vector space over a finite field with $q$ elements, which satisfies $|E|>q$. There exist $x,y\in E$ such that $|E\cdot (y-x)|>q/2.$ In particular, $(E+E)\cdot (E-E)={\mathbb{F}}_q$.

10 pages

References in corpus (1)

• On the distance sets of AD-regular sets