%0 Journal Article
%T The maximal density of product-free sets in Z/nZ
%A Par Kurlberg
%A Jeffrey C. Lagarias
%A Carl Pomerance
%J Mathematics
%D 2011
%I arXiv
%R 10.1093/imrn/rns014
%X This paper studies the maximal size of product-free sets in Z/nZ. These are sets of residues for which there is no solution to ab == c (mod n) with a,b,c in the set. In a previous paper we constructed an infinite sequence of integers (n_i)_{i > 0} and product-free sets S_i in Z/n_iZ such that the density |S_i|/n_i tends to 1 as i tends to infinity, where |S_i|$ denotes the cardinality of S_i. Here we obtain matching, up to constants, upper and lower bounds on the maximal attainable density as n tends to infinity.
%U http://arxiv.org/abs/1111.2634v2