A note on Landau's formula

Landau proved, for any fixed $x>1$, that $$\sum_{0<\gamma\leq T} x^\rho = -\frac{T}{2\pi} \Lambda(x)+ O(\log T) \quad \text{for} \quad T\to \infty,$$ where $\rho$ runs over the non-trivial zeros of the Riemann zeta function $\zeta(s)$ and $\Lambda(x) =\log p$ if $x=p^m,\ p$ prime and $\Lambda(x) =0$ otherwise. Recently Gonek has obtained a form of the previous formula which is uniform in $T$ and $x$. Here we furnish a uniform version of Landau's formula in which the error term has sharper individual and mean-square estimates.