  The dielectric function for electron gas with parabolic energy bands is
derived in a fractional dimensional space. The static response function shows a
good dimensional dependance. The plasma frequencies are obtained from the roots
of the dielectric functions. The plasma dispersion shows strong dimensional
dependence. It is found that the plasma frequencies in the low dimensional
systems are strongly dependent on the wave vector. It is weakly dependent in
the three dimensional system and has a finite value at zero wave vector.
