Upper bounds on pairs of dot products

Given a large finite point set, $P\subset \mathbb R^2$, we obtain upper bounds on the number of triples of points that determine a given pair of dot products. That is, for any pair of positive real numbers, $(α, β)$, we bound the size of the set $\left\{(p,q,r)\in P \times P \times P : p \cdot q = α, p \cdot r = β\right\}.$

No reviews yet.

No comments yet.