On the equivalence relations of α-continued fractions

Hitoshi Nakada, Rie Natsui

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We compare the equivalence relations on real numbers arising from having eventually agreeing α-continued fraction expansion (for each 0 ≤ α ≤ 1) with those from sharing GL(2,Z)- or SL(2,Z)-orbits. We show that the α-relation and the GL(2,Z)-relation of x are identical for any α > 0 when x is of unbounded type. On the other hand, they are not identical for x of bounded type.

Original languageEnglish
Pages (from-to)800-815
Number of pages16
JournalIndagationes Mathematicae
Volume25
Issue number4
DOIs
Publication statusPublished - 2014 Jun 27

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Equivalence relation
Continued fraction
Continued Fraction Expansion
Sharing
Orbit

Keywords

  • Continued fractions
  • Diophantine approximations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the equivalence relations of α-continued fractions. / Nakada, Hitoshi; Natsui, Rie.

In: Indagationes Mathematicae, Vol. 25, No. 4, 27.06.2014, p. 800-815.

Research output: Contribution to journalArticle

Nakada, Hitoshi ; Natsui, Rie. / On the equivalence relations of α-continued fractions. In: Indagationes Mathematicae. 2014 ; Vol. 25, No. 4. pp. 800-815.
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