Article Dans Une Revue American Journal of Mathematics Année : 2014

Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds

Résumé

For convex co-compact hyperbolic manifolds $\Gamma\backslash \mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies $\delta_\Gamma< n/2$, we show that the high-frequency Eisenstein series associated to a point $\xi$ ''at infinity'' concentrate microlocally on a measure supported by (the closure of) the set of points in the unit cotangent bundle corresponding to geodesics ending at $\xi$. The average in $\xi$ of these limit measures equidistributes towards the Liouville measure.

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hal-00608699 , version 1 (13-07-2011)

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Colin Guillarmou, Frederic Naud. Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds. American Journal of Mathematics, 2014, 136 (2), pp.445-479. ⟨10.1353/ajm.2014.0015⟩. ⟨hal-00608699⟩
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