  The effects of electron-electron interactions on the bulk tunneling density
of states (TDOS) are studied near the integer quantum Hall transitions (IQHT).
Taking into account the dynamical screening of the interactions in the critical
conducting state, we show that the behavior of the TDOS is significantly
altered from its noninteracting counterpart. For Coulomb interaction, we
demonstrate that the TDOS vanishes linearly at the Fermi level according to a
quantum Coulomb gap form with a nonuniversal slope. For short-range
interactions, the TDOS is found to follow a power-law with an exponent
proportional to the interaction strength. Since short-range interactions are
known to be irrelevant perturbations at the non-interacting critical point, we
predict that upon scaling, the power-law is smeared, leading to a finite zero
bias TDOS. However, the approach to the zero-bias value is described by a
power-law with a universal exponent determined by the scaling dimension of
short-range interactions. We also consider the case of quasi-1D samples with
edges and find that the TDOS becomes dependent of the Hall conductance due to
an altered boundary condition for diffusion. For short-range interactions, the
TDOS of a quasi-1D strip is linear near the Fermi level with a slope inversely
proportional to the resistivity in the perturbative limit. These results are in
qualitative agreement with the bulk tunneling experiments. We discuss recent
developments in understanding the role played by electron-electron interactions
at the IQHT and the implications of these results on dynamical scaling of the
transition width. We argue that for the long-range Coulomb interaction, the
existence of the quantum Coulomb gap in the quantum critical regime of the
transition gives rise to the observed dynamical exponent z=1.
