论文标题
在Turán猜想和随机乘法功能上
On a Turán conjecture and random multiplicative functions
论文作者
论文摘要
我们表明，如果$ f $是随机完全乘法函数，则$ \ sum_ {n \ le x} \ frac {f（n）} {n} $的可能性至少为$ 1-10^{ - 45} $，而严格小于$ 1 $。对于大$ x $，我们证明了$ o（\ exp（ - \ exp（\ frac {\ log x}} {c \ log \ log x}）））$的渐近上限）$在特定截断为负的特定可能性上，其中$ c $是一个正常的常数。
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.
