On some mean values for the divisor function and the Riemann zeta-function

Let $\Delta(x)$ and $E(x)$ denote respectively the error terms in the summatory formula for the divisor function and the mean square formula for $\zeta (s)$ on the critical line. In this talk we shall discuss some general mean values for $\Delta(x)$ and $E(x)$. From these mean value results, we observe intrinsic difference between these two functions, which suggests that $E(x)$ is more negative then $\Delta(x)$.