Lengths of periods of continued fractions of square roots of integers
type: Item
instance of: scholarly article
title: Lengths of periods of continued fractions of square roots of integers
zbMATH Open document ID: 1208.11013
author: Vładimir I. Arnold
published in: Functional Analysis and Other Mathematics
publication date: 2009-11-02T00:00:00Z
review text: Empirical study of the period length \(T\) of the continued fractions of \(\sqrt{Q}\) (for growing integers \(Q\)) shows several strange asymptotic results, for instance, \(T\leq C \sqrt{Q}\ln Q\). These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11K50
zbMATH DE Number: 5624151
zbMATH Keywords: Gauss-Kuzmin theorem
zbMATH Keywords: odd period lengths of continued fractions
zbMATH Keywords: statistics of continued fractions
reviewed by: Oleg Karpenkov
MaRDI profile type: Publication
full work available at URL: s11853-009-0031-x
OpenAlex ID: W1987660240
cites work: Statistics of the periods of continued fractions for quadratic irrationals
DOI: 10.1007/S11853-009-0031-X
description: scientific article; zbMATH DE number 5624151