Congruence Classes in ${\mathbb{F}}_p^2$: Sharp Results via an Energy Approach

Thang Pham, Le Quang Ham, Steven Senger +2

Let $T_k(E)$ denote the set of congruence classes of ordered $k$-tuples of pairwise distinct points of $E$. Let $p\equiv 3(\mathrm{mod}4)$ be prime. For $E\subset {\mathbb{F}}_p^2$ with $3\leq|…