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Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 2, April 2014
- pp. 445-479
- 10.1353/ajm.2014.0015
- Article
- Additional Information
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For convex co-compact hyperbolic manifolds $\Gamma\backslash{\Bbb H}^{n+1}$ 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 is the Liouville measure.