On the equivalence relations of α-continued fractions

Hitoshi Nakada, Rie Natsui

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Issue number4
Publication statusPublished - 2014 Jun 27
Externally publishedYes


  • Continued fractions
  • Diophantine approximations

ASJC Scopus subject areas

  • Mathematics(all)


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