On the quotient set of the distance set

A. Iosevich, D. Koh, H. Parshall

Let ${\mathbb{F}}_q$ be a finite field of order $q.$ We prove that if $d\ge 2$ is even and $E\subset {\mathbb{F}}_q^d$ with $|E|\ge 9q^{\frac{d}{2}}$ then $$ {\Bbb F}_q=\frac{Δ(E)}{Δ(E)}…