Effective equidistribution for some unipotent flows in $PSL(2, \mathbb{R})^k$ mod cocompact, irreducible lattice

Abstract

Let $d \geq 2$, and let $\Gamma \subset PSL(2, \mathbb{R})^d$ be an irreducible, cocompact lattice. We prove a sharp estimate up to a logarithmic factor on the rate of equidistribution of coordinate horocycle flows on $\Gamma \backslash PSL(2, \mathbb{R})^d$.