On multiplicative functions resembling the Möbius function

Abstract

For multiplicative functions f resembling the Möbius function μ, we establish an upper bound for |∑n≤xf(n)| on much weaker assumptions on f which is comparable with the upper bound for |M(x):=∑n≤xμ(n)| being obtained on assuming the Riemann Hypothesis and using the analytic properties of the generating function 1ζ(s).