  Using the dynamical mean-field theory (DMFT) we study the paramagnetic phase
of the Hubbard model with the density of states (DOS) corresponding to the
three-dimensional cubic lattice and the two-dimensional square lattice, as well
as a DOS with inverse square root singularity. We show that the electron
correlations rapidly smooth out the square-root van Hove singularities (kinks)
in the spectral function for the 3D lattice and that the Mott metal-insulator
transition (MIT) as well as the magnetic-field-induced MIT differ only little
from the well-known results for the Bethe lattice. The consequences of the
logarithmic singularity in the DOS for the 2D lattice are more dramatic. At
half filling, the divergence pinned at the Fermi level is not washed out, only
its integrated weight decreases as the interaction is increased. While the Mott
transition is still of the usual kind, the magnetic-field-induced MIT falls
into a different universality class as there is no field-induced localization
of quasiparticles. In the case of a power-law singularity in the DOS at the
Fermi level, the power-law singularity persists in the presence of interaction,
albeit with a different exponent, and the effective impurity model in the DMFT
turns out to be a pseudo-gap Anderson impurity model with a hybridization
function which vanishes at the Fermi level. The system is then a generalized
Fermi liquid. At finite doping, regular Fermi liquid behavior is recovered.
