论文标题
高阶levin-feinleib定理
A higher order Levin-Feinleib theorem
论文作者
论文摘要
如果仅限于某些非负乘法功能，例如F，在数量上限制并消失在非平方整数上时，我们的结果为我们提供了$ \ sum_ {n \ le x} f（n \ le x} f（n）/n $，带有错误项$ o（（\ log x）因为我们有$ \ sum_ {p \ le q} f（p）（\ log p）/p =κ\ log q+η+o（1/（\ log2q）^h）$（\ log2q）^h）$ for非负$κ$和一些非负整数$ h $。该方法概括了1967年的Levin和Fainleib的诉求，并使用微分方程。
When restricted to some non-negative multiplicative function, say f, bounded on primes and that vanishes on non square-free integers, our result provides us with an asymptotic for $\sum_{n \le X}f(n)/n$ with error term $O((\log X)^{κ-h-1+\varepsilon})$ (for any positive $\varepsilon>0$) as soon as we have $\sum_{p\le Q}f(p)(\log p)/p=κ\log Q+η+O(1/(\log2Q)^h)$ for a non-negative $κ$ and some non-negative integer $h$. The method generalizes the 1967-approach of Levin and Fainleib and uses a differential equation.
