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Large fluctuations of extended Rademacher random multiplicative functions
Let $f$ be an extended Rademacher random multiplicative function (RMF). We show that, for every fixed deterministic function $V(x)$ tending to infinity, almost surely there are arbitrarily large $x$ for which \[ \sum_{n\leq x}f(n) \geq \frac{\sqrt{x}(\log\log x)^{1/4}}{V(x)}. \] The correspondin
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