On a generalization of Markoff's theory.
type: Item
instance of: scholarly article
title: On a generalization of Markoff's theory.
zbMATH Open document ID: 0714.11039
DOI: 10.1016/S0022-314X(05)80038-1
author: Serge Perrine
published in: Journal of Number Theory
publication date: 1991-01-01T00:00:00Z
review text: The author generalizes the phenomenon of Markoff forms using the equation \[ (-\epsilon_ 1A)m^ 2+\epsilon_ 2m^ 2_ 1+\epsilon_ 1m^ 2_ 2=(a+r+1)mm_ 1m_ 2 \] for \(\epsilon =\pm 1\). Using results of \textit{R. Remak} [Math. Ann. 92, 155--182 (1924; JFM 50.0099.02)] and \textit{J. W. S. Cassels} [An introduction to diophantine approximation, Cambridge Tract 45 (1957; Zbl 0077.04801)], he constructs trees of forms for which the Markoff spectrum accumulates at \(1/N\) (for integers \(N>3\)).
reviewed by: Harvey Cohn
Mathematics Subject Classification ID: 11J06
Mathematics Subject Classification ID: 11D09
zbMATH DE Number: 4175040
zbMATH Keywords: approximation constants
zbMATH Keywords: Markoff forms
zbMATH Keywords: Markoff spectrum
MaRDI profile type: Publication
cites work: Q3241280
cites work: Q3993084
description: scientific article; zbMATH DE number 4175040