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

Marco Aymone

doi:10.1016/j.jnt.2019.10.025

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

Number Theory 2019-11-22 v1

Authors: Marco Aymone

View on arXiv ↗ PDF ↗ DOI ↗

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.

Keywords

multiplicative functions prime number theory prime numbers

Cite

@article{arxiv.1908.11014,
  title  = {A note on multiplicative functions resembling the M\"obius function},
  author = {Marco Aymone},
  journal= {arXiv preprint arXiv:1908.11014},
  year   = {2019}
}

Comments

8 pages, submitted to JNT in August, 2018

Related papers

View all related →