An upper bound on the multiplicative energy

Abstract

We prove that the sumset or the productset of any finite set of real numbers, $A,$ is at least $|A{|}^{4/3-\epsilon },$ improving earlier bounds. Our main tool is a new upper bound on the multiplicative energy, $E(A,A).$

Cited by in corpus (4)

• The sum-product phenomenon in arbitrary rings
• Sums and products along sparse graphs
• k-fold sums from a set with few products
• On sums and products in C[x]