Spectral analysis of the Laplacian on geometrically finite hyperbolic manifolds

Details Spectral analysis of the Laplacian on geometrically finite hyperbolic manifolds Spectral analysis of the Laplacian on geometrically finite hyperbolic manifolds

2010-02-10

arxiv.org/abs/1002.2165v1

Mathematics

Spectral Theory

Scientific paper

For geometrically finite hyperbolic manifolds $\Gamma\backslash H^{n+1}$, we
prove the meromorphic extension of the resolvent of Laplacian, Poincar\'e
series, Einsenstein series and scattering operator to the whole complex plane.
We also deduce the asymptotics of lattice points of $\Gamma$ in large balls of
$H^{n+1}$ in terms of the Hausdorff dimension of the limit set of $\Gamma$.

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