一个算术函数的误差项估计

Estimate on an error term of an arithmetic function

设Ψ(n)是Dedekind函数,∑n≤xnΨ(n)=αx+E(x),其中α是常数,E(x)是误差项.主要目的是利用经典的复积分理论及解析方法研究了E(x)的平方积分均值,得到了一个较为精确的估计式.

Let Ψ(n) be the Dedekind totient function.It is known that∑n≤xnΨ(n)=αx+E(x),where α is a constant and E(x) is the error term.The main purpose of this paper is to study the square integral mean value of E(x) by means of classical complex integral theory and analytic method,and give a more precise asymptotic formula.