Some metric properties of α-continued fractions

Hitoshi Nakada, Rie Natsui

研究成果: Article査読

8 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)287-300
ページ数14
ジャーナルJournal of Number Theory
97
2
DOI
出版ステータスPublished - 2002 12 1

ASJC Scopus subject areas

  • 代数と数論

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