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Almost sure upper bound for random multiplicative functions
Published 3 Apr 2023 in math.NT and math.PR | (2304.00943v2)
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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