A remark on Sarnak's conjecture

TL;DR

This paper examines Sarnak's conjecture concerning the Möbius function, focusing on cases where the test function indicates integers with a specific value of a real additive function.

Contribution

It provides new insights into Sarnak's conjecture by analyzing indicator functions related to real additive functions.

Findings

Supports the conjecture in specific cases

Identifies conditions for the conjecture to hold

Contributes to understanding the behavior of the Möbius function

Abstract

We investigate Sarnak's conjecture on the M\"obius function in the special case when the test function is the indicator of the set of integers for which a real additive function assumes a given value.