Sarnak's conjecture implies the Chowla conjecture along a subsequence

TL;DR

This paper demonstrates that if zero entropy dynamical systems are disjoint from the Möbius function, then there exists a subsequence along which the Chowla conjecture on autocorrelations of the Möbius function is valid.

Contribution

It establishes a link between Sarnak's conjecture and the Chowla conjecture, showing that one implies the other along a subsequence.

Findings

Existence of a subsequence satisfying Chowla's conjecture under Möbius disjointness

Connection between zero entropy dynamical systems and autocorrelation properties of Möbius function

Implication of Sarnak's conjecture for Chowla conjecture along a subsequence

Abstract

We show that the M\"obius disjointess of zero entropy dynamical systems implies the existence of an increasing sequence of positive integers along which the Chowla conjecture on autocorrelations of the M\"obius function holds.