A note on multiplicative functions resembling the Möbius function

Marco Aymone

doi:10.1016/j.jnt.2019.10.025

paper

A note on multiplicative functions resembling the Möbius function

arXiv:1908.11014 · doi:10.1016/j.jnt.2019.10.025

Abstract

We provide examples of multiplicative functions $f$ supported on the squarefree integers, such that on primes $f (p) = \pm 1$ and such that $M_{f} (x) := \sum_{n \leq x} f (n) = o (x)$ . Further, by assuming the Riemann hypothesis (RH) we can go beyond $x$ -cancellation.

8 pages, submitted to JNT in August, 2018