Distances from points to planes

P. Birklbauer, A. Iosevich, T. Pham

We prove that if $E\subset {\mathbb{F}}_q^d$, $d\ge 2$, $F\subset \mathrm{Graff}(d-1,d)$, the set of affine $d-1$-dimensional planes in ${\mathbb{F}}_q^d$, then $|Δ(E,F)| \ge \fra…