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

TL;DR

This paper establishes a near-optimal rate of equidistribution for coordinate horocycle flows in certain high-dimensional quotients of PSL(2, R), advancing understanding of unipotent dynamics in these spaces.

Contribution

It provides a sharp estimate, up to a logarithmic factor, on the rate of equidistribution for unipotent flows in cocompact, irreducible lattices in PSL(2, R)^d.

Findings

Derived a sharp estimate for equidistribution rate

Extended results to higher-dimensional PSL(2, R)^d spaces

Improved understanding of unipotent flow dynamics

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 $\Gamma \backslash PSL(2, \mathbb{R})^d$.