Counting Horoballs and Rational Geodesics |
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| Authors: | Belabas Karim; Hersonsky Sa'ar; Paulin Frederic |
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| Institution: | Laboratoire de Mathématiques, UMR 8628 CNRS, Bât. 425, Université Paris-Sud 91405 Orsay Cedex, France; Karim.Belabas{at}math.u-psud.fr, Frederic.Paulin{at}math.u-psud.fr
Department of Mathematics, Ben Gurion University Beer-Sheva, Israel; saarh{at}math.bgu.ac.il |
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| Abstract: | Let M be a geometrically finite pinched negatively curved Riemannianmanifold with at least one cusp. The asymptotics of the numberof geodesics in M starting from and returning to a given cusp,and of the number of horoballs at parabolic fixed points inthe universal cover of M, are studied in this paper. The caseof SL(2, Z), and of Bianchi groups, is developed. 2000 MathematicsSubject Classification 53C22, 11J06, 30F40, 11J70. |
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