A Note on Helson's Conjecture on Moments of Random Multiplicative Functions

Abstract

In this note we are interested in cancellations in sums of multiplicative functions. It is well known that M(x) := Σ n≤x µ(n) = 0(x^(1/2+ε) is equivalent to the Riemann Hypothesis. On the other hand, it is also a classical result that M(x) > x^(1/2+ε) for a sequence of arbitrarily large x. It is in fact conjectured that lim x→ ∞ M(x)/ √x(log log log x)^(5/4) = ±B for some constant B > 0 (see [21]).

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