On quadratic numbers and forms, and Markoff theory
type: Item
instance of: scholarly article
title: On quadratic numbers and forms, and Markoff theory
zbMATH Open document ID: 1478.11094
author: Christophe Reutenauer
published in: Journal of Number Theory
publication date: 2021-07-05T00:00:00Z
review text: Let \(\alpha\) be a root of quadratic polynomial with integer coefficients and \(\frac {p_n}{q_n}\) its partials. Then the author proves that \(\alpha - \frac {p_n}{q_n}=\frac 1{aq_n^2(1+\sqrt{1+\frac 1{bq_n^2}})}\), where \(a\) and \(b\) are constants depending on the character of the number \(\alpha\). The numbers \(a\) and \(b\) are described in detail. He applies this on the Markoff theory and obtains several interesting results.
Mathematics Subject Classification ID: 11J06
Mathematics Subject Classification ID: 11E16
zbMATH DE Number: 7367587
zbMATH Keywords: Markoff theory
zbMATH Keywords: continued fractions
zbMATH Keywords: indefinite binary quadratic forms
zbMATH Keywords: Lagrange numbers
zbMATH Keywords: Christoffel words
zbMATH Keywords: irrationality measure
reviewed by: Jaroslav Hančl
MaRDI profile type: Publication
full work available at URL: j.jnt.2021.03.005
OpenAlex ID: W3154979563
Wikidata QID: Q114157073
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DOI: 10.1016/J.JNT.2021.03.005
description: scientific article; zbMATH DE number 7367587