Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds

Colin Guillarmou; Frederic Naud

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arXiv · 1107.2655

Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds

Colin Guillarmou·Frederic Naud

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Abstract

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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BibTeX RIS

Colin Guillarmou, Frederic Naud. 2011-07-13. Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds. https://arxiv.org/abs/1107.2655

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