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 language | English (US) |
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Pages (from-to) | 1-28 |
Number of pages | 28 |
Journal | International Journal of Number Theory |
Volume | 16 |
Issue number | 1 |
DOIs | |
State | Published - Feb 1 2020 |
Keywords
- Ducci iterates
- Farey fractions
- plane visible points
- similar ordering
ASJC Scopus subject areas
- Algebra and Number Theory