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

Published 27 Oct 2015 in math.CO | (1510.07918v2)

Abstract: Let $E \subseteq \mathbb{F}_q2$ 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, $(E+E) \cdot (E-E) = \mathbb{F}_q$.

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Authors (1)

  1. Giorgis Petridis 

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