广义的Landau误差项研究

New results on error term of generalized Landau

设 φ( n)是 Euler函数 ,r是正整数 .以 E( x;r)表示和式∑n≤ x( nφ( n) ) r的渐近公式中的误差项 ,本文研究了 E( x;r)

Let φ(n) be the Eulers function and r a positive integer. Denote by E(x;r) the error term in the asymptotic formula for the sum ∑n≤x(nφ(n)) r. Two forms of mean value estimates for E(x;r) are obtained.