Möbius Disjointness for product flows of rigid dynamical systems and affine linear flows

2021/01/25 by Wei, Fei · 1 citation
#11N37 #37A44 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2101.10134

Abstract

We obtain that Sarnak's Möbius Disjointness Conjecture holds for product flows between affine linear flows on compact abelian groups of zero topological entropy and a class of rigid dynamical systems. To prove this, we show an estimate for the average value of the product of the Möbius function and any polynomial phase over short intervals and arithmetic progressions simultaneously. In addition, we prove that the logarithmically averaged Möbius Disjointness Conjecture holds for the product flow between any affine linear flow on a compact abelian group of zero entropy and any rigid dynamical system. As an application, we show that the logarithmically averaged Möbius Disjointness Conjecture holds for every Lipschitz continuous skew product dynamical system on \mathbbT² over a rotation of the circle.

Cited by

• Almost Countable Spectrum and Logarithmic Sarnak Conjecture

Related

• Rigidity in dynamics and Möbius disjointness
• Sarnak's Möbius disjointness for dynamical systems with singular spectrum and dissection of Möbius flow
• Measure complexity and Möbius disjointness
• Möbius disjointness for analytic skew products
• Arbitrarily slow decay in the Möbius disjointness conjecture