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 $\mathrm{SL}_2(\mathrm{R}) \times \mathrm{SL}_2(\mathbb{R})$.
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
The Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel
Current address:
School of Mathematics, Institute for Advanced Study, Princeton, NJ
Amir Mohammadi
Department of Mathematics, University of California, San Diego, La Jolla, CA
Current address:
Department of Mathematics, University of California, Berkeley, CA
Zhiren Wang
Department of Mathematics, Pennsylvania State University, University Park. PA
Current address:
Department of Mathematics, Johns Hopkins University, Baltimore, MD
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