IUMJ

Title: Product sets and distance sets of random point sets in vector spaces over finite rings

Authors: Anh vinh Le

Issue: Volume 62 (2013), Issue 3, 911-926

Abstract:

Let $\mathbb{Z}_q=\mathbb{Z}/q\mathbb{Z}$ be the finite cyclic ring of $q$ elements, where $q$ is an odd prime power. For almost all subsets $\mathcal{E},\mathcal{F}\subset\mathbb{Z}_q^d$ of cardinality $|\mathcal{E}|=|\mathcal{F}|\geq Cq$ for some large constant $C>0$, we show that the product set and distance set between $\mathcal{E}$ and $\mathcal{F}$ contain all non-units of $\mathbb{Z}_q$.