A note on multiplicative functions resembling the M\"obius function

Marco Aymone

arXiv:1908.11014·math.NT·November 22, 2019

A note on multiplicative functions resembling the M\"obius function

Marco Aymone

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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.

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