Three-point configurations determined by subsets of ${\mathbb{F}}_q^2$ via the Elekes-Sharir paradigm

Michael Bennett, Alex Iosevich, Jonathan Pakianathan

We prove that if $E\subset {\mathbb{F}}_q^2$, $q\equiv 3\mathrm{mod}4$, has size greater than $C{q}^{7/4}$, then $E$ determines a positive proportion of all congruence classes of triangle…