# American Institute of Mathematical Sciences

2017, 11: 155-188. doi: 10.3934/jmd.2017008

## On the rate of equidistribution of expanding horospheres in finite-volume quotients of SL(2, ${\mathbb{C}}$)

 Department of Mathematics, Box 480, Uppsala University, SE-75106 Uppsala, Sweden

Received  December 22, 2015 Revised  December 02, 2016 Published  February 2017

Let $\Gamma$ be a lattice in $G=\mathrm{SL}(2, \mathbb{C})$. We give an effective equidistribution result with precise error terms for expanding translates of pieces of horospherical orbits in $\Gamma\backslash G$. Our method of proof relies on the theory of unitary representations.

Citation: Samuel C. Edwards. On the rate of equidistribution of expanding horospheres in finite-volume quotients of SL(2, ${\mathbb{C}}$). Journal of Modern Dynamics, 2017, 11: 155-188. doi: 10.3934/jmd.2017008
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