Some distribution results of the Oppenheim continued fractions
type: Item
instance of: scholarly article
title: Some distribution results of the Oppenheim continued fractions
zbMATH Open document ID: 1381.11061
author: Yuanyang Chang
author: Jihua Ma
published in: Monatshefte für Mathematik
publication date: 2017-10-27T00:00:00Z
review text: In this paper, the authors are mainly concerned with the distribution properties of the Oppenheim continued fraction expansions. The first result is a Gauss-Kuzumin-Lévy type theorem, which is concerned with the conditional distribution function as well as its conditional density with respect to the basic intervals. The second result deals with the asymptotic distribution of the sequence of partial maxima of some stationary process in extreme value theory. This result shows a Fréchet law concerning this type, extending previous work of \textit{J. Galambos} [Q. J. Math., Oxf. II. Ser. 23, 147--151 (1972; Zbl 0234.10041)] and \textit{W. Philipp} [Acta Arith. 28, 379--386 (1976; Zbl 0332.10033)] on the regular continued fraction expansion. The third result concerns a uniform distribution modulo \(1\).
reviewed by: Takao Komatsu
Mathematics Subject Classification ID: 11K55
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 6798866
zbMATH Keywords: Oppenheim continued fraction
zbMATH Keywords: Gauss-Kuzumin-Lévy type theorem
zbMATH Keywords: growth rate of digits
zbMATH Keywords: Fréchet Law
zbMATH Keywords: uniform distribution modulo \(1\)
MaRDI profile type: Publication
full work available at URL: s00605-017-1050-1
OpenAlex ID: W2605722226
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DOI: 10.1007/S00605-017-1050-1
description: scientific article; zbMATH DE number 6798866