论文标题
在涉及一般算术函数和积分零件函数的总和上
On a sum involving general arithmetic functions and the integral part function
论文作者
论文摘要
令$ f $为满足一些简单条件的算术功能。本文的目的是为数量\ [s_f（x）：= \ sum_ {n \ leq x} \ frac {f（[x/n]）} {[x/n]} \]作为$ x \ rightArrow \ rightArrow \ rightarrow \ infty $，$ [x/n]} \]的目的是建立一个渐近公式。这概括了Bordellès，Dai，Heyman，Pan和Shparlinski的最新结果。
Let $f$ be an arithmetic function satisfying some simple conditions. The aim of this paper is to establish an asymptotical formula for the quantity \[ S_f(x):=\sum_{n\leq x}\frac{f([x/n])}{[x/n]} \] as $x\rightarrow\infty$, where $[t]$ is the integral part of the real number $t$. This generalizes some recent results of Bordellès, Dai, Heyman, Pan and Shparlinski.
