On a Tur\'an conjecture and random multiplicative functions
| Autor: | Angelo, Rodrigo, Xu, Max Wenqiang |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We show that if $f$ is the random completely multiplicative function, the probability that $\sum_{n\le x}\frac{f(n)}{n}$ is positive for every $x$ is at least $1-10^{-45}$, while also strictly smaller than $1$. For large $x$, we prove an asymptotic upper bound of $O(\exp(-\exp( \frac{\log x}{C\log \log x })))$ on the exceptional probability that a particular truncation is negative, where $C$ is some positive constant. Comment: V3: accepted version, typos and minor mistakes corrected |
| Databáze: | arXiv |
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