On an Error Term of Chowla, I Original Research Article

LetE(x; r) be the error term in the mean-value estimate of (phi(n)/n)r, wherephi(n) is the Euler totient function, andris a positive real number. We show thatimageand∫x1 E(t; r)dt=O(xvar epsilon(x; r)),wherecis a positive constant, andvar epsilon(x; r) is a certain function tending to 0 asx→∞. These results generalize those of Pillai and Chowla and of Suryanarayana and Sitaramachandrarao forr=1.