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arXiv · 2304.00943

Almost sure upper bound for random multiplicative functions

Rachid Caich
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Abstract

Let $\varepsilon >0$. Let $f$ be a Steinhaus or Rademacher random multiplicative function. We prove that we have almost surely, as $x \to +\infty$, $$ \sum_{n \leqslant x} f(n) \ll \sqrt{x} (\log_2 x)^{\frac{3}{4}+ \varepsilon}. $$

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Rachid Caich. 2023-04-03. Almost sure upper bound for random multiplicative functions. https://arxiv.org/abs/2304.00943

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