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

TL;DR

This paper proves Sarnak's M"obius disjointness conjecture for a class of skew product dynamical systems on a circle and the Heisenberg nilmanifold, extending previous results by removing symmetry restrictions.

Contribution

It establishes the conjecture for a broader class of systems by eliminating the symmetry condition previously assumed in earlier work.

Findings

Proves M"obius disjointness for skew products on circle and Heisenberg nilmanifold.

Extends previous results by removing symmetry restrictions.

Broadens the applicability of Sarnak's conjecture in dynamical systems.

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.