On exponential densities and limit ratios of subsets of N

J. Li; L. Olsen

doi:10.1007/s00009-020-01559-7

On exponential densities and limit ratios of subsets of N

J. Li, L. Olsen

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

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).

Original language	English
Article number	122
Number of pages	17
Journal	Mediterranean Journal of Mathematics
Volume	17
DOIs	https://doi.org/10.1007/s00009-020-01559-7
Publication status	Published - 28 Jun 2020

Keywords

Positive integer sequence
Exponential densities
Limit ratios

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10.1007/s00009-020-01559-7Licence: CC BY

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Cite this

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title = "On exponential densities and limit ratios of subsets of N",

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).",

keywords = "Positive integer sequence, Exponential densities, Limit ratios",

author = "J. Li and L. Olsen",

note = "Funding: National Natural Science Foundation of China (11671189,11971109).",

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AU - Li, J.

AU - Olsen, L.

N1 - Funding: National Natural Science Foundation of China (11671189,11971109).

PY - 2020/6/28

Y1 - 2020/6/28

N2 - 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).

AB - 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).

KW - Positive integer sequence

KW - Exponential densities

KW - Limit ratios

U2 - 10.1007/s00009-020-01559-7

DO - 10.1007/s00009-020-01559-7

M3 - Article

SN - 1660-5446

VL - 17

JO - Mediterranean Journal of Mathematics

JF - Mediterranean Journal of Mathematics

M1 - 122

ER -

On exponential densities and limit ratios of subsets of N

Abstract

Keywords

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