Rank of Matrices with Entries from a Multiplicative Group

Abstract

Abstract We establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative group of small rank. Applying these bounds we show that the distance sets of finite pointsets in $\mathbb {R}^d$ generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets.

Locations

• International Mathematics Research Notices - View
• arXiv (Cornell University) - View - PDF