论文标题
显式平均无平方支持的功能：到卷积方法的边缘
Explicit averages of square-free supported functions: to the edge of the convolution method
论文作者
论文摘要
We give a general statement of the convolution method so that one can provide explicit asymptotic estimations for all averages of square-free supported arithmetic functions that have a sufficiently regular order on the prime numbers and observe how the nature of this method gives error term estimations of order $X^{-δ}$, where $δ$ belongs to an open real positive set $I$.为了获得更好的误差估计，一个自然的问题是，我们是否可以达到关键顺序的错误项$ x^{ - δ_0} $，其中$Δ_0$（关键指数）是$ i $的右手端点。我们通过提出一种新方法来积极回答这个问题，该方法在某些规律性条件下几乎在质量上几乎所有实例进行了质量改进；现在，可以用其关键指数和合理的显式误差常数给出备受言论的无方算术功能的平均值的渐近估计。我们通过分析与Ramaré-Akhilesh（2017）的工作相关的特定平均值来说明这种新方法，该平均水平在施加非平凡的相对性条件时会导致显着改善。
We give a general statement of the convolution method so that one can provide explicit asymptotic estimations for all averages of square-free supported arithmetic functions that have a sufficiently regular order on the prime numbers and observe how the nature of this method gives error term estimations of order $X^{-δ}$, where $δ$ belongs to an open real positive set $I$. In order to have a better error estimation, a natural question is whether or not we can achieve an error term of critical order $X^{-δ_0}$, where $δ_0$, the critical exponent, is the right hand endpoint of $I$. We reply positively to that question by presenting a new method that improves qualitatively almost all instances of the convolution method under some regularity conditions; now, the asymptotic estimation of averages of well-behaved square-free supported arithmetic functions can be given with its critical exponent and a reasonable explicit error constant. We illustrate this new method by analyzing a particular average related to the work of Ramaré--Akhilesh (2017), which leads to notable improvements when imposing non-trivial coprimality conditions.
