Tunneling into a Two-Dimensional Electron Liquid in a Weak Magnetic Field

We study the spectral density function of a two-dimensional electron liquid in a weak magnetic field, filling factor ν1. A hydrodynamic model for low-energy excitations of the liquid is developed. It is found that even at ν1 the tunneling density of states exhibits a gap at low energies. Its width 2E₀ depends on the strength of interaction only logarithmically, ${2E}₀{{0ex}{0ex}}={{0ex}{0ex}}({}{{ω}}c/{ν})ln({ν}{e}²/{ε}{}{v}F)$. The effects of temperature and disorder on the density of states are discussed.