论文标题
分数总和的双曲线总和
Hyperbolic Summation for Fractional Sums
论文作者
论文摘要
令$ f（n）$为算术函数，对于[0,1）$中的某些$α\，让$ \ lfloor。\ rfloor $表示整数零件函数。 In this paper, we evaluate asymptotically the sums $$\sum_{n_{1}n_{2}\leq x}f \left( \left\lfloor \frac{x}{n_{1}n_{2}} \right\rfloor \right),$$ we use the estimation of three-dimensional exponential sums due致罗伯特和萨尔戈斯。
Let $f(n)$ be an arithmetic function with $f(n) \ll n^α$ for some $α\in[0,1)$ and let $\lfloor .\rfloor $ denote the integer part function. In this paper, we evaluate asymptotically the sums $$\sum_{n_{1}n_{2}\leq x}f \left( \left\lfloor \frac{x}{n_{1}n_{2}} \right\rfloor \right),$$ we use the estimation of three-dimensional exponential sums due to Robert and Sargos.
