The semiconductor hole gas can be viewed as the companion of the classic interacting electron gas with a more complicated band structure and plays a crucial role in the understanding of ferromagnetic semiconductors. Here we study the dielectric function of a homogeneous hole gas in zinc blende III-V bulk semiconductors within random phase approximation with the valence band being modeled by Luttinger's Hamiltonian in the spherical approximation. In the static limit we find a beating of Friedel oscillations between the two Fermi momenta for heavy and light holes, while at large frequencies dramatic corrections to the plasmon dispersion occur. Copyright (C) EPLA, 2010