Products of Differences in Prime Order Finite Fields

Abstract

There exists an absolute constant $C$ with the following property. Let $A\subseteq {\mathbb{F}}_p$ be a set in the prime order finite field with $p$ elements. Suppose that $|A|>C{p}^{5/8}$. The set \[ (A \pm A)(A \pm A) = \{(a_1 \pm a_2)(a_3 \pm a_4) : a_1,a_2,a_3,a_4 \in A\} \] contains at least $p/2$ elements.

14 pages

References in corpus (2)

• Growth Estimates in Positive Characteristic via Collisions
• A point-line incidence identity in finite fields, and applications

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