Pinned algebraic distances determined by Cartesian products in 𝔽_{𝕡}²

Petridis, Giorgis

doi:10.1090/proc/13649

Pinned algebraic distances determined by Cartesian products in $\mathbb {F}_p^2$
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Proc. Amer. Math. Soc. 145 (2017), 4639-4645 Request permission

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.

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