优化的与Euler函数有关的误差项的算术均值

The Count Average Value of Optimal Error Term Which is Connected with Euler Function

设ρ(n)是Euler函数,r正实数,则有其中a是与r有关的常数,而以(x;r)是误差项,本文的主要目的是利用经典的复积分理论及解析的方法研究了E(x;r)的算术均值,得到了一个较为精确的估计式。

Letφ (n) be the Euler totient function, and r is a positive real number. It is known that where a is a constant related to r and E(x;r) is the error term. The main purpose is using the calssical complex integral theory and the analytic method to study the arithmetic value of E(x ; r) , and a more preices asymptotic formula.