Quotient and product sets of thin subsets of the positive integers |
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| Authors: | Javier Cilleruelo D S Ramana O Ramaré |
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| Institution: | 1.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM) and Departamento de Matemáticas,Universidad Autónoma de Madrid,Madrid,Spain;2.Harish-Chandra Research Institute,Jhunsi, Allahabad,India;3.CNRS / Institut de Mathématiques de Marseille,Aix Marseille Université,Marseille Cedex 9,France |
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| Abstract: | We study the cardinalities of A/A and AA for thin subsets A of the set of the first n positive integers. In particular, we consider the typical size of these quantities for random sets A of zero density and compare them with the sizes of A/A and AA for subsets of the shifted primes and the set of sums of two integral squares. |
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