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

Abstract

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

12 pages. This is part of an expanded paper titled "Exponential multiple mixing for some partially hyperbolic flows on products of $PSL(2,\mathbb{R}$)," published in DCDS - A, 2018, 38 (3) : 989-1006

References in corpus (2)

• On effective equidistribution for higher step nilflows
• Effective equidistribution of horocycle lifts