On the Discretized Sum-Product Problem

Abstract

Abstract We give a new proof of the discretized ring theorem for sets of real numbers. As a special case, we show that if $A\subset \mathbb {R}$ is a $(\delta ,1/2)_1$-set in the sense of Katz and Tao, then either $A+A$ or $A.A$ must have measure at least $|A|^{1-\frac {1}{68}}$.

Locations

• International Mathematics Research Notices - View
• arXiv (Cornell University) - View - PDF
• DSpace@MIT (Massachusetts Institute of Technology) - View - PDF