Mobius disjointness conjecture on the product of a circle and the Heisenberg nilmanifold

TL;DR

This paper proves that the Möbius function is linearly disjoint from certain distal skew product systems on the product of a circle and a Heisenberg nilmanifold, extending previous results in the field.

Contribution

It generalizes recent work by Huang-Liu-Wang by establishing Möbius disjointness for a broader class of systems on the circle and Heisenberg nilmanifold.

Findings

Möbius function is linearly disjoint from specific distal skew products

Extension of previous disjointness results to Heisenberg nilmanifold

Broader class of dynamical systems analyzed for Möbius disjointness

Abstract

Let $\mathbb{T}$ be the unit circle and $\Gamma\setminus G$ the 3-dimensional Heisenberg nilmanifold. We prove that the M\"obius function is linearly disjoint from a class of distal skew products on $\mathbb{T}\times\Gamma\setminus G$. These results generalize a recent work of Huang-Liu-Wang.