Conditions pour que les entiers de Beurling aient une densité

Abstract : In 1997 H.G.Diamond gave a condition on Beurling’s generalized prime numbers in order that the corresponding generalized integers have a density. We give a new proof of this condition (Theorem 1) and a proof that it is not necessary (Theorem 2 and Examples). However, it is very near to be necessary (Theorem 3). Both proofs of Theorems 1 and 2 rely on Fourier analysis, mainly the Wiener algebra, and partly on probability methods.
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Submitted on : Monday, November 14, 2016 - 4:48:11 PM
Last modification on : Wednesday, January 23, 2019 - 2:39:26 PM
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  • HAL Id : hal-01393875, version 1
  • ARXIV : 1611.04432

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Jean-Pierre Kahane. Conditions pour que les entiers de Beurling aient une densité. 2016. ⟨hal-01393875⟩

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