A bound on the multiplicative energy of a sum set and extremal sum-product problems

Abstract

In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool is a new result which provides a nontrivial upper bound on the multiplicative energy of a sum set or difference set.

13 pages

References in corpus (3)

• On the Erdos distinct distance problem in the plane
• Using the subspace theorem to bound unit distances
• On the Minkowski distances and products of sum sets