Markov and Lagrange spectra (survey of the literature)

DOI10.1007/BF01213889zbMath0453.10031MaRDI QIDQ1148951

A. V. Malyshev

Publication date: 1981

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

bibliographyBibliographyLagrange spectrumMarkov spectrumminima of indeterminate binary quadratic forms

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to number theory (11-02) Continued fractions and generalizations (11J70) Minima of forms (11H50) Homogeneous approximation to one number (11J04)

Related Items (5)

Diophantine approximation on conics ⋮ The hyperbolic geometry of Markov's theorem on Diophantine approximation and quadratic forms ⋮ Conway topograph, -dynamics and two-valued groups ⋮ Vectors of a given Diophantine type. II ⋮ Markov and Lagrange spectra for Laurent series in $1/T$ with rational coefficients

Cites Work

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• The largest gaps in the lower Markoff spectrum
• One-sided minima of indefinite binary quadratic forms and one-sided diophantine approximations
• On the lower Markov spectrum
• Diophantine approximation of complex numbers
• The connection between the Lagrange and Markoff spectra
• Über die Menge der Zahlen, die als Minima quadratischer Formen auftreten
• Diophantische Approximationen in imaginären quadratischen Zahlkörpern, insbesondere im Körper \(K(i\sqrt 2)\)
• On c-minimal forms
• Noncoincidence of the Markov and Lagrange spectra
• Markoff forms and primitive words
• Fuchssche Gruppen, die freies Produkt zweier zyklischer Gruppen sind, und die Gleichung \(x^2+y^2+z^2=xyz\).
• On the sum and product of continued fractions
• The Markoff chain
• Über einen Perronschen Satz
• Approach to Markoff's minimal forms through modular functions
• Diophantine Approximation and Horocyclic Groups
• On the Approximation of Quaternions.
• More numerical evidence on the uniqueness of Markov Numbers
• The Uniqueness of the Markoff Numbers
• Minimum of quadratic forms with respect to Fuchsian groups. II.
• Quadratic Irrationals in the Lower Lagrange Spectrum
• The Hausdorff-Besicovich Dimension of the Level Sets of Person's Modular Function
• Farey Triangles and Farey Quadrangels in the Complex Plane.
• On the Lower Range of Perron's Modular Function
• Farey Simplices in the Space of Quaternions.
• Sums and Products of Continued Fractions
• Representation of Markoff's binary quadratic forms by geodesics on a perforated torus
• Sums of Sets of Continued Fractions
• Some Numerical Evidence Concerning the Uniqueness of the Markov Numbers
• Note on the Minimum of an Indefinite Binary Quadratic Form
• On the sums of continued fractions
• On M. Hall's Continued Fraction Theorem
• Diophantische Approximationen in imaginär quadratischen Zahlkörpern
• ON THE MINIMUM OF A BILINEAR FORM
• THE MINIMUM OF AN INDEFINITE BINARY QUADRATIC FORM
• Sur l'approximation des nombres complexes par les nombres des corps imaginaires quadratiques dénués d'idéaux non principaux particulièrement lorsque vaut l'algorithme d'Euclide
• The minima of indefinite binary quadratic forms

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