A note on multiplicative functions resembling the Möbius function

Abstract

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

arXiv comment8 pages, submitted to JNT in August, 2018

References in corpus (2)

• Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function
• Correlations of multiplicative functions and applications

Cited by in corpus (2)

• Multiplicative functions that are close to their mean
• Partial sums of random multiplicative functions and extreme values of a model for the Riemann zeta function