Incidences and pairs of dot products

Ben Lund

Let $\mathbb{F}$ be a field, let $P\subseteq {\mathbb{F}}^d$ be a finite set of points, and let $\alpha ,\beta \in \mathbb{F}\setminus \{0\}$. We study the quantity \[|Π_{α, β}| = \{(p,q,r) \…