The Lindelöf Hypothesis for Zeta Zero Ordinates

We provide conditional and unconditional asymptotic formulae for the exponential sums ${\sum }_{\gamma }{\gamma }^{-i\tau }$, where the summation is over the ordinates of the nontrivial zeros $\rho =\beta +i\gamma$ of the Riemann zeta-function. In particular, the obtained results are related to the Lindelöf Hypothesis for these ordinates (in the sense of Gonek et al. [10]).