Some metric properties of \(\alpha\)-continued fractions.
type: Item
instance of: scholarly article
title: Some metric properties of \(\alpha\)-continued fractions.
zbMATH Open document ID: 1067.11043
DOI: 10.1016/S0022-314X(02)00008-2
author: Hitoshi Nakada
author: Rie Natsui
published in: Journal of Number Theory
publication date: 2003-04-02T00:00:00Z
review text: Borel-Bernstein theorem is one of the metrical theorems on the partial quotients of the regular continued fractions. There are also some almost everywhere properties, which were shown by \textit{H, G. Diamond} and \textit{J. D. Vaaler} [Pac. J. Math. 122, 73--82 (1986; Zbl 0589.10056)] or by \textit{W. Philipp} [Acta Arith. 28, 379--386 (1976; Zbl 0332.10033)]. In this paper, the authors show that these metrical properties also hold for any \(\alpha\)-continued fraction for \(1/2\leq\alpha<1\). It is a modification of the nearest integer continued fractions taking \(n\) as the integer part of \(y\) when \(y\in[n-1+\alpha,n+\alpha)\) for \(1/2\leq\alpha\leq 1\), instead of the nearest integer.
reviewed by: Takao Komatsu
Mathematics Subject Classification ID: 11K50
zbMATH DE Number: 1891443
zbMATH Keywords: \(\alpha\)-continued fractions
zbMATH Keywords: Borel-Bernstein theorem
zbMATH Keywords: Maxima of continued fraction coefficients
zbMATH Keywords: Metrical theory of continued fractions
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1891443