论文标题
在某些数字理论上
On certain sums of number theory
论文作者
论文摘要
我们研究形状$ \ sum_ {n \ leqslant x} f \ left（\ lfloor x/n \ rfloor \ right）$的总和，其中$ f $是von mangoldt函数或dirichlet-piltz divisor函数。当$ f =λ$和$ f =τ$时，我们改进了先前的估计，并在$ f =τ_r$的情况下提供新的结果，并在每种情况下打破$ \ frac {1} {2} $ - 在每种情况下打破$ \ frac {1} {2} $。还研究了功能$ f =μ^2 $，$ f = 2^ω$和$ f =ω$。
We study sums of the shape $\sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right)$ where $f$ is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We improve previous estimates when $f = Λ$ and $f = τ$, and provide new results when $f = τ_r$ with $r \geqslant 3$, breaking the $\frac{1}{2}$-barrier in each case. The functions $f=μ^2$, $f=2^ω$ and $f=ω$ are also investigated.
