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April 2019 On Diamond’s L1 Criterion for Asymptotic Density of Beurling Generalized Integers
Gregory Debruyne, Jasson Vindas
Michigan Math. J. 68(1): 211-223 (April 2019). DOI: 10.1307/mmj/1548903624

Abstract

We give a short proof of the L1 criterion for Beurling generalized integers to have a positive asymptotic density. We in fact prove the existence of density under a weaker hypothesis. We also discuss related sufficient conditions for the estimate m(x)=nkxμ(nk)/nk=o(1) with the Beurling analog μ of the Möbius function.

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Gregory Debruyne. Jasson Vindas. "On Diamond’s L1 Criterion for Asymptotic Density of Beurling Generalized Integers." Michigan Math. J. 68 (1) 211 - 223, April 2019. https://doi.org/10.1307/mmj/1548903624

Information

Received: 12 April 2017; Revised: 3 November 2017; Published: April 2019
First available in Project Euclid: 31 January 2019

zbMATH: 07155464
MathSciNet: MR3934610
Digital Object Identifier: 10.1307/mmj/1548903624

Subjects:
Primary: 11N80
Secondary: 11M41 , 11M45 , 11N37

Rights: Copyright © 2019 The University of Michigan

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Vol.68 • No. 1 • April 2019
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