Journal of Modern Dynamics (JMD)

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

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

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Samuel C. Edwards - Department of Mathematics, Box 480, Uppsala University, SE-75106 Uppsala, Sweden (email)

Abstract: 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.

Keywords:  Effective equidistribution, translates, horospheres.
Mathematics Subject Classification:  Primary: 37A17; Secondary: 11F03.

Received: December 2015;      Revised: December 2016;      Available Online: February 2017.