An improved bound on the number of dot products determined by a finite point set in the plane

We are interested to bound from below the number of distinct dot products determined by a finite set of points P in the Euclidean plane. In this paper, we build on [3] to obtain the improved lower bound | { p ⋅ q : p , q ∈ P } | ≳ | P | 2 3 + 7 1425 .