M\"{o}bius disjointness for topological models of ergodic systems with discrete spectrum

TL;DR

This paper establishes a criterion ensuring disjointness conditions in Sarnak's M"obius Disjointness Conjecture and proves the conjecture for topological models of ergodic systems with discrete spectrum.

Contribution

It introduces a new criterion for disjointness and confirms the conjecture for a broad class of topological models with discrete spectrum.

Findings

The conjecture holds for topological models of ergodic systems with discrete spectrum.

A new criterion for disjointness in the context of the conjecture.

Validation of the conjecture extends to systems with discrete spectrum.

Abstract

We provide a criterion for a point satisfying the required disjointness condition in Sarnak's M\"obius Disjointness Conjecture. As a direct application, we have that the conjecture holds for any topological model of an ergodic system with discrete spectrum.