Helson's problem for sums of a random multiplicative function

Abstract

We consider the random functions $S_N(z):={\sum }_{n=1}^{N}z(n)$, where $z(n)$ is the completely multiplicative random function generated by independent Steinhaus variables $z(p)$. It is shown that $\mathbb{E}|S_N|\gg \sqrt{N}(\log N{)}^{-0.05616}$ and that $(\mathbb{E}|S_N{|}^q{)}^{1/q}{\gg }_q\sqrt{N}(\log N{)}^{-0.07672}$ for all $q>0$.

This version of the paper has been accepted for publication in Mathematika

References in corpus (1)

• An inequality of Hardy--Littlewood type for Dirichlet polynomials

Cited by in corpus (5)

• Moments of polynomials with random multiplicative coefficients
• Weak product spaces of Dirichlet series
• Pseudomoments of the Riemann zeta function
• Idempotent Fourier multipliers acting contractively on $H^p$ spaces
• Moments of random multiplicative functions over function fields