The maximal density of product-free sets in Z/nZ
Number Theory
2013-09-10 v2
Abstract
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.
Cite
@article{arxiv.1111.2634,
title = {The maximal density of product-free sets in Z/nZ},
author = {Par Kurlberg and Jeffrey C. Lagarias and Carl Pomerance},
journal= {arXiv preprint arXiv:1111.2634},
year = {2013}
}
Comments
Minor typos corrected. To appear in IMRN