论文标题
平滑的省总价函数的误差术语的分布
The Distribution of Error Terms of Smoothed Summatory Totient Functions
论文作者
论文摘要
我们考虑适用于合适的平滑操作员的应用后的基本功能的插入功能，并研究相关误差项的限制行为。在一些有条件的假设下，我们表明平滑的误差项通过Akbary-ng-shahabi合并的框架具有限制对数分布。为了获得此结果，我们证明了perron的反转公式的截断版本，用于任意riesz的典型手段。我们以有条件的证据结论，即平滑运算符的至少两个应用是必要的，足以以$ \ sqrt {x} $绑定错误项的增长。
We consider the summatory function of the totient function after applications of a suitable smoothing operator and study the limiting behavior of the associated error term. Under several conditional assumptions, we show that the smoothed error term possesses a limiting logarithmic distribution through a framework consolidated by Akbary--Ng--Shahabi. To obtain this result, we prove a truncated version of Perron's inversion formula for arbitrary Riesz typical means. We conclude with a conditional proof that at least two applications of the smoothing operator are necessary and sufficient to bound the growth of the error term by $\sqrt{x}$.
