On exponential densities and limit ratios of subsets of N

Li, J.; Olsen, L.

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dc.contributor.author	Li, J.
dc.contributor.author	Olsen, L.
dc.date.accessioned	2020-07-01T16:30:03Z
dc.date.available	2020-07-01T16:30:03Z
dc.date.issued	2020-06-28
dc.identifier.citation	Li , J & Olsen , L 2020 , ' On exponential densities and limit ratios of subsets of N ' , Mediterranean Journal of Mathematics , vol. 17 , 122 . https://doi.org/10.1007/s00009-020-01559-7	en
dc.identifier.issn	1660-5446
dc.identifier.other	PURE: 268530542
dc.identifier.other	PURE UUID: 8753949d-9431-4214-8151-9ad2271564e6
dc.identifier.other	ORCID: /0000-0002-8353-044X/work/76777164
dc.identifier.other	WOS: 000543710800001
dc.identifier.other	Scopus: 85087026957
dc.identifier.uri	http://hdl.handle.net/10023/20188
dc.description	Funding: National Natural Science Foundation of China (11671189,11971109).	en
dc.description.abstract	Given 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.format.extent	17
dc.language.iso	eng
dc.relation.ispartof	Mediterranean Journal of Mathematics	en
dc.rights	Copyright © 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 http://creativecommons.org/licenses/by/4.0/.	en
dc.subject	Positive integer sequence	en
dc.subject	Exponential densities	en
dc.subject	Limit ratios	en
dc.subject	QA Mathematics	en
dc.subject	T-NDAS	en
dc.subject.lcc	QA	en
dc.title	On exponential densities and limit ratios of subsets of N	en
dc.type	Journal article	en
dc.description.version	Publisher PDF	en
dc.contributor.institution	University of St Andrews.Pure Mathematics	en
dc.identifier.doi	https://doi.org/10.1007/s00009-020-01559-7
dc.description.status	Peer reviewed	en

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