A new perspective on the distance problem over prime fields

Alex Iosevich, Doowon Koh, Thang Pham

Let ${\mathbb{F}}_p$ be a prime field, and $\mathcal{E}$ a set in ${\mathbb{F}}_p^2$. Let $\Delta (\mathcal{E})=\{||x-y||:x,y\in \mathcal{E}\}$, the distance set of $\mathcal{E}$. In…