# 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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