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COUNTING HOROBALLS AND RATIONAL GEODESICS

Published online by Cambridge University Press:  23 October 2001

KARIM BELABAS ,
SA'AR HERSONSKY  and
FRÉDÉRIC PAULIN
KARIM BELABAS
Affiliation:
Laboratoire de Mathématiques, UMR 8628 CNRS, Bât. 425, Université Paris-Sud, 91405 Orsay Cedex, France; [email protected], [email protected]
SA'AR HERSONSKY
Affiliation:
Department of Mathematics, Ben Gurion University, Beer-Sheva, Israel; [email protected]
FRÉDÉRIC PAULIN
Affiliation:
Laboratoire de Mathématiques, UMR 8628 CNRS, Bât. 425, Université Paris-Sud, 91405 Orsay Cedex, France; [email protected], [email protected]
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Abstract

Let M be a geometrically finite pinched negatively curved Riemannian manifold with at least one cusp. The asymptotics of the number of geodesics in M starting from and returning to a given cusp, and of the number of horoballs at parabolic fixed points in the universal cover of M, are studied in this paper. The case of SL(2, ℤ), and of Bianchi groups, is developed.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 5 , September 2001 , pp. 606 - 612
Copyright
© The London Mathematical Society 2001

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