This paper determines the order of magnitude of low moments of Steinhaus and Rademacher random multiplicative functions, proving Helson's conjecture about better-than-squareroot cancellation in the first moment. This result also disproves counter-conjectures and has implications for limit distribution and large deviations of these functions, leveraging a connection to critical multiplicative chaos.

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This paper presents a significant contribution to the field of analytic number theory by resolving a long-standing conjecture about random multiplicative functions. The rigorous mathematical analysis, detailed proofs, and the novel connection to multiplicative chaos theory warrant a high rating. The paper's impact is enhanced by disproving previous counter-conjectures and offering potential avenues for future research. While the technical nature of the content may limit its accessibility, the paper's contribution to the field is undeniable.