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dc.contributor.authorLi, J.
dc.contributor.authorOlsen, L.
dc.identifier.citationLi , J & Olsen , L 2020 , ' On exponential densities and limit ratios of subsets of N ' , Mediterranean Journal of Mathematics , vol. 17 , 122 .
dc.identifier.otherPURE: 268530542
dc.identifier.otherPURE UUID: 8753949d-9431-4214-8151-9ad2271564e6
dc.identifier.otherORCID: /0000-0002-8353-044X/work/76777164
dc.identifier.otherWOS: 000543710800001
dc.identifier.otherScopus: 85087026957
dc.descriptionFunding: National Natural Science Foundation of China (11671189,11971109).en
dc.description.abstractGiven α,β,γ∈[0,1] with α≤β, we prove that there exists a subset of N such that its lower and upper exponential densities and its lower and upper limit ratios are equal to α, β, γ and 1, respectively. This result provides an affirmative answer to an open problem posed by Grekos et al. (Unif Distrib Theory 6:117–130, 2011).
dc.relation.ispartofMediterranean Journal of Mathematicsen
dc.rightsCopyright © The Author(s) 2020. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit
dc.subjectPositive integer sequenceen
dc.subjectExponential densitiesen
dc.subjectLimit ratiosen
dc.subjectQA Mathematicsen
dc.titleOn exponential densities and limit ratios of subsets of Nen
dc.typeJournal articleen
dc.description.versionPublisher PDFen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.description.statusPeer revieweden

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