On maximal product sets of random sets
نویسندگان
چکیده
For every positive integer N and α∈[0,1), let B(N,α) denote the probabilistic model in which a random set A⊂{1,…,N} is constructed by choosing independently element of {1,…,N} with probability α. We prove that, as N⟶+∞, for A we have |AA|∼|A|2/2 1−o(1), if only iflog(α2(logN)log4−1)loglogN⟶−∞. This improves on theorem Cilleruelo, Ramana Ramaré, who proved above asymptotic between |AA| |A|2/2 when α=o(1/logN), supplies complete characterization maximal product sets sets.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2021
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2021.01.008