Exciton spectrum for two-dimensional electron systems at fractional occupation numbers of the Landau levels

It is shown that q absorption lines arise in two-dimensional crystal lattices at a rational fractional number p/q of magnetic-field flux quanta per electron. The absorption lines correspond to different exciton formation energies and are determined by the electron-hole Coulomb interaction. The number of the absorption lines is calculated for electron densities corresponding to the fractional quantum Hall effect.