Quotient and product sets of thin subsets of the positive integers

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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Submitted on : Thursday, June 29, 2017 - 5:11:39 PM
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Javier Cilleruelo, D. S. Ramana, Olivier Ramaré. Quotient and product sets of thin subsets of the positive integers. Proceedings of the Steklov Institute of Mathematics, MAIK Nauka/Interperiodica, 2017, 296 (1), pp.52 - 64. ⟨10.1134/S0081543817010059⟩. ⟨hal-01550708⟩

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