A note on multiplicative functions resembling the Möbius function

Marco Aymone

doi:10.1016/j.jnt.2019.10.025

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arXiv · 1908.11014

A note on multiplicative functions resembling the Möbius function

Marco Aymone

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Abstract

We provide examples of multiplicative functions $f$ supported on the squarefree integers, such that on primes $f(p)=\pm1$ and such that $M_f(x):=\sum_{n\leq x} f(n)=o(\sqrt{x})$. Further, by assuming the Riemann hypothesis (RH) we can go beyond $\sqrt{x}$-cancellation.

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Marco Aymone. 2019-08-29. A note on multiplicative functions resembling the Möbius function. https://doi.org/10.1016/j.jnt.2019.10.025

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