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arXiv · 2303.06774

Better than square-root cancellation for random multiplicative functions

Max Wenqiang Xu
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Abstract

We investigate when the better than square-root cancellation phenomenon exists for $\sum_{n\le N}a(n)f(n)$, where $a(n)\in \mathbb{C}$ and $f(n)$ is a random multiplicative function. We focus on the case where $a(n)$ is the indicator function of $R$ rough numbers. We prove that $\log \log R \asymp (\log \log x)^{\frac{1}{2}}$ is the threshold for the better than square-root cancellation phenomenon to disappear.

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Max Wenqiang Xu. 2023-03-12. Better than square-root cancellation for random multiplicative functions. https://arxiv.org/abs/2303.06774

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