Product Sets and Distance Sets of Random Point Sets in Vector Spaces Over Finite Rings

摘要

Let Z_q = Z/qZ be the finite cyclic ring of q elements, where q is an odd prime power. For almost all subsets E,F ? Z_q~d of cardinality |E| = |F| ≥ Cq for some large constant C > 0, we show that the product set and distance set between E and F contain all non-units of Z_q.