On an error term of Chowla .1.

[摘要] Let E(x;r) be the error term in the mean-value estimate of (phi(n)/n)(r), where phi(n) is the Euler totient function, and I is a positive real number. We show that Sigma(n less than or equal to x) E(n;r) = cx + O(x epsilon(x;r)), and integral(1)(x) E(t;r)dt = O(x epsilon(x;r)), where c is a positive constant, and epsilon(x;r) is a certain function tending to 0 as x --> infinity. These results generalize those of Pillai and Chowla and of Suryanarayana and Sitaramachandrarao for r=1. (C) 1997 Academic Press.

[发布日期] 1997-05-01