Ducci iterates and similar ordering of visible points in convex regions

Junxian Li, Albert Tamazyan, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

Hardy et al. first introduced the notion of similar ordering of pairs of rationals, and Mayer proved that pairs of Farey fractions in FQ are similarly ordered when Q is large enough. We generalize Mayer's result to Ducci iterates of Farey sequence and visible points in certain regions in the plane. We also study the distribution of values of generalized indices of these sequences.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalInternational Journal of Number Theory
Volume16
Issue number1
DOIs
StatePublished - Feb 1 2020

Keywords

  • Ducci iterates
  • Farey fractions
  • plane visible points
  • similar ordering

ASJC Scopus subject areas

  • Algebra and Number Theory

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