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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

SALVATORE COSENTINO
Affiliation:
IMPA - Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina, 110 - Jardim Botânico, Rio de Janeiro - RJ, 22460-320 Brasil (e-mail: [email protected])

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.

Type
Research Article
Copyright
1999 Cambridge University Press

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