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Article Dans Une Revue Proceedings - Mathematical Sciences Année : 2022

The number of rationals determined by large sets of sifted integers

Résumé

We prove that the number of fractions h 1 / h 2 of integers h 1 , h 2 a subset A ⊂ H∩[1, X ] is at least α X/(log X) 3/2 , where H is the set p −1, p being a prime such that p +1 is a sum of two coprime squares. So, this number of fractions is ε α 1+ε |A| 2 , where ε is any positive real number. We take this opportunity to describe a geometrical view of the sieve and its usage to study integer sequences.
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Dates et versions

hal-04057230 , version 1 (04-04-2023)

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Olivier Ramaré. The number of rationals determined by large sets of sifted integers. Proceedings - Mathematical Sciences, 2022, 132, ⟨10.1007/s12044-022-00698-z⟩. ⟨hal-04057230⟩
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