Möbius disjointness for skew products on a circle and a nilmanifold

Abstract

Let $\mathbb{T}$ be the unit circle and $\Gamma \backslash G$ the $3$-dimensional Heisenberg nilmanifold. We prove that a class of skew products on $\mathbb{T}\times \Gamma \backslash G$ are distal, and that the Möbius function is linearly disjoint from these skew products. This verifies the Möbius Disjointness Conjecture of Sarnak.

28 pages

References in corpus (1)

• The Mobius disjointness conjecture for distal flows