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arXiv · 1411.6388

Helson's problem for sums of a random multiplicative function

Andriy Bondarenko·Kristian Seip
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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 ${\Bbb E} |S_N|\gg \sqrt{N}(\log N)^{-0.05616}$ and that $({\Bbb E} |S_N|^q)^{1/q}\gg_{q} \sqrt{N}(\log N)^{-0.07672}$ for all $q>0$.

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Andriy Bondarenko, Kristian Seip. 2015-05-22. Helson's problem for sums of a random multiplicative function. https://doi.org/10.1112/s0025579315000236

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