The cohomological equation and invariant distributions for horocycle maps

@inproceedings{Tanis2014TheCE,
  title={The cohomological equation and invariant distributions for horocycle maps},
  author={James Tanis},
  year={2014}
}
We study the invariant distributions for the horocycle map on $\Gamma\backslash SL(2, \mathbb{R})$ and prove Sobolev estimates for the cohomological equation of the horocycle map. As an application, we obtain an estimate for the rate of equidistribution for horocycle maps on compact manifolds. 

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