Pinned algebraic distances determined by Cartesian products in ${\mathbb{F}}_p^2$

Abstract

Let $p$ be an odd prime and $A\subseteq {\mathbb{F}}_p$ be a subset of the finite field with $p$ elements. We show that $A\times A\subseteq {\mathbb{F}}_p^2$ determines at least a constant multiple of $\min \{p,|A{|}^{3/2}\}$ distinct pinned algebraic distances.

9 pages. Minor corrections compared to the first version

References in corpus (1)

• Products of Differences in Prime Order Finite Fields