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Equidistribution of parabolic fixed points in the limit set of Kleinian groups
Published online by Cambridge University Press: 01 December 1999
Abstract
We show that the Patterson–Sullivan measure on the limit set of a geometrically finite Kleinian group with cusps can be recovered as a weak limit of sums of Dirac masses placed on an appropriate orbit of each parabolic fixed point. A corollary is a sharp asymptotic estimate for a natural counting function associated to a cuspidal subgroup. We also discuss the connection between the above counting and the Riemann hypothesis in some examples of arithmetical lattices.
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- Research Article
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- 1999 Cambridge University Press
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