An improvement on the number of simplices in ${\mathbb{F}}_q^d$

Thang Pham, Duc Hiep Pham, Anh Vinh Le

Let $\mathcal{E}$ be a set of points in ${\mathbb{F}}_q^d$. Bennett, Hart, Iosevich, Pakianathan, and Rudnev (2016) proved that if $|\mathcal{E}|\gg q^{d-\frac{d-1}{k+1}}$ then $\mat…