  We study rotating homogeneous turbulent convection forced by a mean vertical
temperature gradient by means of direct numerical simulations (DNS) in the
Boussinesq approximation in a rotating frame. In the absence of rotationour
results are in agreement with the "ultimate regime of thermal convection" for
the scaling of the Nusselt and Reynolds numbers vs Rayleigh and Prandtl
numbers. Rotation is found to increase both $Nu$ and $Re$ at fixed $Ra$ with a
maximum enhancement for intermediate values of the Rossby numbers,
qualitatively similar, but with stronger intensity, to what observed in
Rayleigh-B\'enard rotating convection. Our results are interpreted in terms of
a quasi-bidimensionalization of the flow with the formation of columnar
structures displaying strong correlation between the temperature and the
vertical velocity fields.
