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The Markov spectra for Fuchsian groups


Author: L. Ya. Vulakh
Journal: Trans. Amer. Math. Soc. 352 (2000), 4067-4094
MSC (2000): Primary 11J06, 11F06
DOI: https://doi.org/10.1090/S0002-9947-00-02455-7
Published electronically: April 17, 2000
MathSciNet review: 1650046
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Abstract: Applying the Klein model $D^2$ of the hyperbolic plane and identifying the geodesics in $D^2$ with their poles in the projective plane, the author develops a method of determining infinite binary trees in the Markov spectrum for a Fuchsian group. The method is applied to a maximal group commensurable with the modular group and other Fuchsian groups.


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Additional Information

L. Ya. Vulakh
Affiliation: Department of Mathematics, The Cooper Union, 51 Astor Place, New York, New York 10003
Email: vulakh@cooper.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02455-7
Keywords: Diophantine approximation, projective geometry, hyperbolic geometry
Received by editor(s): September 17, 1997
Received by editor(s) in revised form: August 25, 1998
Published electronically: April 17, 2000
Article copyright: © Copyright 2000 American Mathematical Society

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