Abstract
We prove effective equidistribution theorems, with polynomial error rate, for orbits of the unipotent subgroups of $\mathrm{SL}_2(\mathbb{R})$ in arithmetic quotients of $\mathrm{SL}_2(\mathbb{C})$ and $\mathrm{SL}_2(\mathbb{R})\times\mathrm{SL}_2(\mathbb{R})$.
The proof is based on the use of a Margulis function, tools from incidence geometry,
and the spectral gap of the ambient space.
Authors
Elon Lindenstrauss
Institute for Advanced Study, 1 Einstein Drive, Princeton, NJ 08540, USA and The Einstein Institute of Mathematics, Edmund J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel
Amir Mohammadi
Department of Mathematics, University of California, Berkeley, CA 94720-3840, USA
Zhiren Wang
Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA
