On exponential densities and limit ratios of subsets of N

J. Li, L. Olsen

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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 languageEnglish
Article number122
Number of pages17
JournalMediterranean Journal of Mathematics
Volume17
DOIs
Publication statusPublished - 28 Jun 2020

Keywords

  • Positive integer sequence
  • Exponential densities
  • Limit ratios

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