Mutual position of two smooth quadrics over finite fields

Shamil Asgarli, Chi Hoi Yip

Given two irreducible conics $C$ and $D$ over a finite field ${\mathbb{F}}_q$ with $q$ odd, we show that there are $q^2/4+O(q^{3/2})$ points $P$ in ${\mathbb{P}}^2({\mathbb{F}}_q)$ such…