Z/nZ中乘积自由集的最大密度
The maximal density of product-free sets in Z/nZ
摘要：
本文研究了Z/nZ中无积集的最大尺寸。这些是剩余的集合，对于这些剩余的集合，没有ab == c（mod n）的解，其中a，b，c在集合中。在前一篇文章中，我们构造了Z/n_iZ中整数（n_i）_{i > 0}和无积集S_i的无穷序列，使得当i趋于无穷大时密度|S_i| /n_i趋于1，其中|S_i| $表示S_i的基数。在这里，我们得到匹配，常数，上限和下界的最大可达到的密度n趋于无穷大。
英文摘要：
This paper studies the maximal size of product-free sets in Z/nZ. These are sets of residues for which there is no solution to ab == c (mod n) with a,b,c in the set. In a previous paper we constructed an infinite sequence of integers (n_i)_{i > 0} and product-free sets S_i in Z/n_iZ such that the density |S_i|/n_i tends to 1 as i tends to infinity, where |S_i|$ 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.
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