Conditions for Beurling's integers to have a density
Number Theory
2016-11-15 v1
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.
Keywords
Cite
@article{arxiv.1611.04432,
title = {Conditions for Beurling's integers to have a density},
author = {Jean-Pierre Kahane},
journal= {arXiv preprint arXiv:1611.04432},
year = {2016}
}
Comments
in French