On a generalization of Markoff’s theory. (Sur une généralisation de la théorie de Markoff.) (French) Zbl 0714.11039

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 R. Remak [Math. Ann. 92, 155–182 (1924; JFM 50.0099.02)] and 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 \(N>3\)).
Reviewer: Harvey Cohn


11J06 Markov and Lagrange spectra and generalizations
11D09 Quadratic and bilinear Diophantine equations
Full Text: DOI


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[3] Remak, R., Uber indefinite binäre quadratische minimal Formen, Math. Ann., 92, 155-182 (1924) · JFM 50.0099.02
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