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arXiv · 1704.03771

On Diamond's $L^1$ criterion for asymptotic density of Beurling generalized integers

Gregory Debruyne·Jasson Vindas
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Abstract

We give a short proof of the $L^{1}$ criterion for Beurling generalized integers to have a positive asymptotic density. We actually prove the existence of density under a weaker hypothesis. We also discuss related sufficient conditions for the estimate $m(x)=\sum_{n_{k}\leq x} \mu(n_k)/n_k=o(1)$, with $\mu$ the Beurling analog of the Moebius function.

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Gregory Debruyne, Jasson Vindas. 2017-04-12. On Diamond's $L^1$ criterion for asymptotic density of Beurling generalized integers. https://doi.org/10.1307/mmj/1548903624

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