关于短区间Liouville函数的一个注记
A note on the Liouville function in short intervals
摘要：
本文给出了一个简短而完备的证明，证明了对任何$δ> 0$，$\sum_{x \leq n \leq x+x^δ} λ(n) = o(x^δ)$对几乎所有的$x \in [X, 2X]$ .我们还勾画了这样的结果一般实值乘性函数的证明。这两个结果都是我们最近更复杂和冗长的预印本中结果的特殊情况。
英文摘要：
In this note we give a short and self-contained proof that, for any $δ> 0$, $\sum_{x \leq n \leq x+x^δ} λ(n) = o(x^δ)$ for almost all $x \in [X, 2X]$. We also sketch a proof of a generalization of such a result to general real-valued multiplicative functions. Both results are special cases of results in our more involved and lengthy recent pre-print.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
