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Let N S¹ be the Steinhaus multiplicative function: a completely multiplicative function such that ( (p) ) ₑ₈₌₄ are i. i. d. random variables uniformly distributed on S¹. Helson conjectured that E|₍ ₗ (n) |=o (x) as x, and this was solved in strong form by Harper. We give a short proof of the conjecture using a result of Saksman and Webb on a random model for the Riemann zeta function.
Gorodetsky et al. (Wed,) studied this question.