Multiplicative Functions Resembling the Möbius Function.

A multiplicative function f is said to be resembling the Möbius function if f is supported on the square-free integers, and f (p)= ±1 for each prime p. We prove O- and Ω-results for the summatory function ∑n≤xf(n) for a class of these f, and the point is that these O-results demonstrate cancellations better than the square-root saving. It is proved in particular that the summatory function is O(x1/3+ε) under the Riemann Hypothesis. On the other hand it is proved to be Ω(x1/4) unconditionally. It is interesting to compare these with the corresponding results for the Möbius function. [ABSTRACT FROM AUTHOR]