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.