Counting horoballs and rational geodesics
Abstract
Let M be a geometrically finite pinched negatively curved Riemannian manifold with at least one cusp. We study 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. In the appendix, due to K. Belabas, the case of SL(2,Z) and of Bianchi groups is developed.
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