Transactions of the American Mathematical Society

Farey polytopes and continued fractions associated with discrete hyperbolic groups

Author(s): L. Ya. Vulakh
Journal: Trans. Amer. Math. Soc. 351 (1999), 2295-2323.
MSC (1991): Primary 11J99
Posted: February 5, 1999
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Abstract: The known definitions of Farey polytopes and continued fractions are generalized and applied to diophantine approximation in

-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

is found.

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