On the growth of the denominators of convergents
type: Item
instance of: scholarly article
title: On the growth of the denominators of convergents
zbMATH Open document ID: 0928.11007
DOI: 10.1023/A:1006623805374
published in: Acta Mathematica Hungarica
publication date: 1999-10-31T00:00:00Z
review text: The following result is proved. Let \(\log \frac{1+\sqrt 5}2\leq X\leq Y<\infty\). Then there exist non-enumerable many pairwise not equivalent numbers \(\alpha\) such that \[ \lim_{\overline{n\to \infty}} \frac 1n \log q_n =X\quad \text{and}\quad \overline{\lim_{n\to\infty}} \frac 1n \log q_n= Y, \] where \(q_n\) denotes the denominator of the \(n^{th}\) convergent of \(\alpha\).
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11J70
zbMATH DE Number: 1355144
zbMATH Keywords: continued fraction
zbMATH Keywords: convergents
author: Christoph Baxa
reviewed by: Péter Kiss
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1355144