  We present a theory for carrier induced ferromagnetism in diluted magnetic
semi-conductor (DMS). Our approach treats on equal footing quantum fluctuations
within the RPA approximation and disorder within CPA. This method allows for
the calculation of $T_c$, magnetization and magnon spectrum as a function of
hole, impurity concentration and temperature. It is shown that, sufficiently
close to $T_c$, and within our decoupling scheme (Tyablicov type) the CPA for
the itinerant electron gas reduces to the Virtual Crystal Approximation. This
allows, in the low impurity concentration and low density of carriers to
provide analytical expression for $T_c$. For illustration, we consider the case
of $Ga_{1-c}Mn_{c}As$ and compare our results with available experimental data.
