On an Error Term of Chowla, III 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 integer. We prove in this paper thatE(x; r)=Ω±((log log x)r/2).This generalizes the earlier result of Montgomery.