Distinct dot products, convexity, and AA+1

Abstract: We discuss recent developments in estimating the number of distinct dot products determined by a large finite set of $n$ points in the plane. The improvement comes from improved understanding of the multiplicative structure of an additively shifted product set, $AA+1,$ when $A$ is a large finite subset of the real numbers. This breakthrough was made possible by new additive combinatorial results about convex sets of numbers.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)