论文标题
乘法功能类似于莫比乌斯·funciton
Multiplicative functions resembling the Möbius funciton
论文作者
论文摘要
如果在无方面的整数上支持$ f $，则据说乘法$ f $类似于möbius函数，而每个prime $ p $ $ f（p）= \ pm 1 $。我们证明了$ o $ - 和$ω$ - 用于省点功能的$ \ sum_ {n \ leq x} f（n）$用于Aymone研究的这些$ f $的类别，而关键是这些$ o $ $ $ $ $ $ $ $ $ - 分子表现出比方形储蓄更好的取消。尤其证明，在Riemann假设下，夏季函数为$ O（x^{1/3+\ varepsilon}）$。另一方面，事实证明是$ω（x^{1/4}）$无条件。将它们与Möbius函数的相应结果进行比较很有趣。
A multiplicative function $f$ is said to be resembling the Möbius function if $f$ is supported on the square-free integers, and $f(p)=\pm 1$ for each prime $p$. We prove $O$- and $Ω$-results for the summatory function $\sum_{n\leq x} f(n)$ for a class of these $f$ studied by Aymone, and the point is that these $O$-results demonstrate cancellations better than the square-root saving. It is proved in particular that the summatory function is $O(x^{1/3+\varepsilon})$ under the Riemann Hypothesis. On the other hand it is proved to be $Ω(x^{1/4})$ unconditionally. It is interesting to compare these with the corresponding results for the Möbius function.
