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

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.