A note on Euler's φ{symbol}-function

In this paper we study the asymptotic behaviour of a certain error term linked with Euler's phi function. We prove that certain upper bounds for this error term are equivalent to the Riemann hypothesis, and this is better than previous results obtained by Sitaramachandra ans Suryanarayna. We also prove that (contrary to a suggestion of Pillai and Chowla) the description of the asymptotic behaviour of this error term does not involve knowledge that the Riemann's zeta function has no zero on vertical line sigma=1 (this information can be substituted by the functional equation).