Effective Equidistribution for some Unipotent Flows in PSL(2, R)^k mod Cocompact, Irreducible Lattice

James Tanis

Published 2014-12-17Version 1

Let $k \geq 2$ and $\Gamma \subset \operatorname{PSL}(2, \mathbb R)^k$ be an irreducible, cocompact lattice. We prove effective equidistribution for unipotent flows on $\Gamma \backslash \operatorname{PSL}(2, \mathbb R)^k$ whose generator in $\operatorname{\mathfrak s\mathfrak l}(2, \mathbb R)^k$ satisfies the following condition: As a $2k\times 2k$ matrix, the eigenspace of the zero eigenvalue has codimension 1. These are the simplest cases for proving effective equidistribution in $\Gamma \subset \operatorname{PSL}(2, \mathbb R)^k$.