Product sets and distance sets of random point sets in vector spaces over finite rings Anh vinh Le 05C50Product setsdistance setsfinite ringsrandom point sets 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 $\mathbb{Z}_q$. Indiana University Mathematics Journal 2013 text pdf 10.1512/iumj.2013.62.4943 10.1512/iumj.2013.62.4943 en Indiana Univ. Math. J. 62 (2013) 911 - 926 state-of-the-art mathematics http://iumj.org/access/