Counting horoballs and rational geodesics

Karim Belabas; Sa'ar Hersonsky; Frédéric Paulin

doi:10.1112/S0024609301008244

Counting horoballs and rational geodesics

Karim Belabas, Sa'ar Hersonsky, Frédéric Paulin

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

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.

Original language	English
Pages (from-to)	606-612
Number of pages	7
Journal	Bulletin of the London Mathematical Society
Volume	33
Issue number	5
DOIs	https://doi.org/10.1112/S0024609301008244
State	Published - 1 Jan 2001

ASJC Scopus subject areas

General Mathematics

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title = "Counting horoballs and rational geodesics",

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.",

author = "Karim Belabas and Sa'ar Hersonsky and Fr{\'e}d{\'e}ric Paulin",

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AU - Belabas, Karim

AU - Hersonsky, Sa'ar

AU - Paulin, Frédéric

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N2 - 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.

AB - 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.

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U2 - 10.1112/S0024609301008244

DO - 10.1112/S0024609301008244

M3 - Article

AN - SCOPUS:0013297735

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EP - 612

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

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Counting horoballs and rational geodesics

Abstract

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