Some metric properties of α-continued fractions

Hitoshi Nakada, Rie Natsui

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The α-continued fraction is a modification of the nearest integer continued fractions taking n as the integer part of y when y ε [n - 1 + α, n + α), instead of the nearest integer. For x εo[α - 1, α), we have the following α-continued fraction expansion: with Cn ≥ 1 and εn = ±1 for n ≥ 1. We prove the Borel-Bernstein theorem for α-continued fractions and also discuss some metrical properties related to max1 ≤ n ≤ N Cn. Indeed, we prove that exist and have the same constant for almost every x.

Original languageEnglish
Pages (from-to)287-300
Number of pages14
JournalJournal of Number Theory
Issue number2
Publication statusPublished - 2002 Dec 1
Externally publishedYes


  • Borel-Bernstein theorem
  • Maxima of continued fraction coefficients
  • α-Continued fractions

ASJC Scopus subject areas

  • Algebra and Number Theory


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