The Mattila-Sjölin problem for the k-distance over a finite field

Daewoong Cheong, Hunseok Kang, Jinbeom Kim

Let ${\mathbb{F}}_q^d$ be a $d$-dimensional vector space over a finite field ${\mathbb{F}}_q$ with $q$ elements. For $x\in {\mathbb{F}}_q^d$, let $\Vert x\Vert =x_1^2+\cdots +x_d^2$. By abuse of…