Abstract
We have calculated the frequency dependent dielectric response function for a quantum plasma under a constant magnetic field and a one-dimensional periodic modulation potential. It is found that the original inverse square root divergence in the density of states is removed by the modulation potential while periodic finite peaks and sudden steps are introduced. The electron-hole excitation exhibits two new features due to the periodic modulation. (i) the excitation contains double: peaks at omega around omega(c) and (ii) it also contains a series of kink like structures at the band edges.