On the metrical theory of continued fraction mixing fibred systems and its application to Jacobi-Perron algorithm
type: Item
instance of: scholarly article
title: On the metrical theory of continued fraction mixing fibred systems and its application to Jacobi-Perron algorithm
zbMATH Open document ID: 1026.11066
author: Hitoshi Nakada
author: Rie Natsui
published in: Monatshefte für Mathematik
publication date: 2003-08-20T00:00:00Z
review text: The authors study the metric theory of fibred systems in the case of continued fraction mixing systems. They obtain the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to the theorems for the regular continued fractions, obtained by \textit{J. Galambos} [Q. J. Math., Oxf. II. Ser. 23, 147-151 (1972; Zbl 0234.10041)], by \textit{W. Philipp} [Acta Arith. 28, 379-386 (1976; Zbl 0332.10033)] and by \textit{H. G. Diamond} and \textit{J. D. Vaaler} [Pac. J. Math. 122, 73-82 (1986; Zbl 0589.10056)]. These theorems hold for the Jacobi-Perron algorithm.
Mathematics Subject Classification ID: 11K50
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 1968530
zbMATH Keywords: fibred system
zbMATH Keywords: continued fraction mixing
zbMATH Keywords: Jacobi-Perron algorithm
zbMATH Keywords: metric theory of continued fractions
zbMATH Keywords: stochastic processes
zbMATH Keywords: strong law of large numbers
reviewed by: Takao Komatsu
MaRDI profile type: Publication
full work available at URL: s00605-002-0473-4
OpenAlex ID: W2033969974
DOI: 10.1007/S00605-002-0473-4
description: scientific article; zbMATH DE number 1968530