The Existence of a Distribution Function for an Error Term Related to the Euler Function

Abstract

The average order of the Euler function ϕ(n), the number of integers less than n which are relatively prime to n, raises many difficult and still unanswered questions. Thus, for1.1,and1.2,it is known that R(x) = O(x log x) and H(x) = O(log x). However, though these results are quite old, they were not improved until recently.