Untitled

Abstract

We investigate when the better than square-root cancellation phenomenon exists for n≤N a(n)f (n), where a(n) ∈ C and f (n) is a random multiplicative function. We focus on the case where a(n) is the indicator function of R rough numbers. We prove that log log R (log log x)1 2 is the threshold for the better than square-root cancellation phenomenon to disappear.