论文标题
某些地板功能总和
Certain floor function sums over powers
论文作者
论文摘要
我们研究总和$$ s_f（x）= \ sum_ {n \ leq x} f \ left（\ left \ lfloor \ frac {x} {x} {n} \ right \ rfloor \ right）$这种限制使我们能够对$ s_f（x）$的渐近扩展中的错误项之一进行非平地估计。我们还陈述了与我们的结果有关的几种猜想。
We study the sums $$ S_f(x) = \sum_{n\leq x} f\left(\left\lfloor\frac{x}{n}\right\rfloor\right) $$ when $f$ is supported on $r$th powers with $r\geq 2$. This restriction allows us to give nontrivial estimates for one of the error terms in the asymptotic expansion of $S_f(x)$. We also state several conjectures related to our results.
