Equidistribution of parabolic fixed points in the limit set of Kleinian groups

被引:7
|
作者
Cosentino, S [1 ]
机构
[1] Inst Matemat Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil
关键词
D O I
10.1017/S0143385799152015
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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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页码:1437 / 1484
页数:48
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