M\"obius Disjointness Conjecture for a skew product on a circle and the Heisenberg nilmanifold

Abstract

We establish Sarnak's conjecture on M\"obius disjointness for the dynamical system of a skew product on a circle and the three-dimensional Heisenberg nilmanifold, first studied by Wen Huang, Jianya Liu and Ke Wang. We advance the work of Huang, Liu, Wang, and their followers to a broad generality by removing the previously imposed restrictive symmetry condition.