Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds

Details Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds

2011-07-13

arxiv.org/abs/1107.2655v1

Mathematics

Spectral Theory

25 pages, 1 figure

Scientific paper

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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