Farey polytopes and continued fractions associated with discrete hyperbolic groups
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- by L. Ya. Vulakh PDF
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Abstract:
The known definitions of Farey polytopes and continued fractions are generalized and applied to diophantine approximation in $n$-dimensional euclidean spaces. A generalized Remak-Rogers isolation theorem is proved and applied to show that certain Hurwitz constants for discrete groups acting in a hyperbolic space are isolated. The approximation constant for the imaginary quadratic field of discriminant $-15$ is found.References
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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
- Received by editor(s): February 26, 1996
- Received by editor(s) in revised form: May 19, 1997
- Published electronically: February 5, 1999
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 2295-2323
- MSC (1991): Primary 11J99
- DOI: https://doi.org/10.1090/S0002-9947-99-02151-0
- MathSciNet review: 1467477