论文标题
Selberg-删除方法上的备注
Remarks on the Selberg--Delange method
论文作者
论文摘要
令$ \ varrho $为一个复杂的数字，让$ f $为乘法算术函数，其dirichlet系列采用表格$ζ（s）^\ varrho g（s）$，其中$ g $与多重函数$ g $相关。经典的Selberg-Delange方法提供了$ g $的分析延续的假设，或者在$ g $的分析延续下提供$ f $的平均值，或者在$ s = 1 $的$ g（s）$ $ g（s）$的绝对收敛中。我们考虑了不同的假设，与以前的假设不直接相当，并研究了它们如何产生〜$ f $的平均值急剧渐近估计。
Let $\varrho$ be a complex number and let $f$ be a multiplicative arithmetic function whose Dirichlet series takes the form $ζ(s)^\varrho G(s)$, where $G$ is associated to a multiplicative function $g$. The classical Selberg-Delange method furnishes asymptotic estimates for averages of $f$ under assumptions of either analytic continuation for $G$, or absolute convergence of a finite number of derivatives of $G(s)$ at $s=1$. We consider different set of hypotheses, not directly comparable to the previous ones, and investigate how they can yield sharp asymptotic estimates for the averages of~$f$.
