Let $\Delta(T)$ and $E(T)$ be the error terms in the classical Dirichlet divisor problem and in the asymptotic formula for the mean square of the Riemann zeta function on the critical strip, respectively. We show that $\Delta(T)$ and $E(T)$ are asymptotic integral transforms of each other. We then use this integral representation of $\Delta(T)$ to give a new proof of a result of M. Jutila.