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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Farey polytopes and continued fractions associated with discrete hyperbolic groups


Author: L. Ya. Vulakh
Journal: Trans. Amer. Math. Soc. 351 (1999), 2295-2323
MSC (1991): Primary 11J99
Published electronically: February 5, 1999
MathSciNet review: 1467477
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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.


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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: http://dx.doi.org/10.1090/S0002-9947-99-02151-0
PII: S 0002-9947(99)02151-0
Keywords: Diophantine approximation, Clifford algebra, hyperbolic geometry
Received by editor(s): February 26, 1996
Received by editor(s) in revised form: May 19, 1997
Published electronically: February 5, 1999
Article copyright: © Copyright 1999 American Mathematical Society