The luminescence spectrum of modulation-doped quantum wells is investigated theoretically with regard to the many-body effects caused by the extra conduction electrons. In the zero-temperature limit vertex corrections are shown to be unimportant, so that the emission frequencies are determined by the self-energies of the valence-band holes and the conduction-band electrons. Calculations of the self-energies are carried out perturbationally, using the plasmon-pole approximation for the dielectric function. The electron- and hole-energy levels are also calculated self-consistently by local density-functional theory. The results of both theories agree satisfactorily with each other over a large range of conduction electron densities and explain recent experiments [Pinczuk et al., Surf. Sci. 142, 492 (1984)].