与Dedekind函数Ψ(n)倒数有关的误差项的均值估计  

Mean value estimates of an error term related to the reciprocal of the Dedekind totient function Ψ(n)

作　　者：史美华[1] 

机构地区：[1]浙江教育学院数学系,浙江杭州310012

出　　处：《浙江师大学报（自然科学版）》2001年第3期246-249,共4页Journal of Zhejiang Normal University(Natoral Sciences)

摘　　要：设Ψ ( n)是 Dedekind函数 ,则有∑n≤ xnΨ ( n) =αx +E( x) ,其中α是常数 ,而 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 E( x)的算术均值和积分均值 。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 related error term. The main purpose of this paper was using the classical complex integral theory and the analytic method to study the arithmetic and integral mean value of E(x), and gave a more precis asymptotic formula.

关 键 词：DEDEKIND函数 DIRICHLET级数 误差项 均值估计 倒数 复积分理论 解析方法 算术函数 

分 类 号：O156.4[理学—数学]