  We investigate the effects of correlations on the properties of the ground
state of the rotating harmonically-trapped Bose gas by adding Bogoliubov
fluctuations to the mean-field ground state of an $N$-particle single-vortex
system. We demonstrate that the fluctuation-induced correlations lower the
energy compared to that of the mean-field ground state, that the vortex core is
pushed slightly away from the center of the trap, and that an unstable mode
with negative energy (for rotations slower than a critical frequency) emerges
in the energy spectrum, thus, pointing to a better state for slow rotation. We
construct mean-field ground states of 0-, 1-, and 2-vortex states as a function
of rotation rate and determine the critical frequencies for transitions between
these states, as well as the critical frequency for appearance of a metastable
state with an off-center vortex and its image vortex in the evanescent tail of
the cloud.
