与Dedekind函数ψ(n)有关的误差项的性质

On an error term related to the Dedekind totient function

设Ψ (n)是 Dedekind函数 .首先对和式∑n≤ xΨ (n)n 的渐近公式中的误差项作了改进 ,以 E(x)表示改进后的误差项 ,进一步研究了 E(x)

Let Ψ(n) be the Dedekind totient function. In this paper,we improve the error term in the asymptotic formula for the sum ∑n≤xΨ(n)n , with E(x) denoting the improved error term in the formula. Two forms of mean value estimates for E(x) are obtained.