QCD improved parton distribution functions of ${\mathbf{\gamma^*_L}}$
  QCD corrections to the QED formula for parton distribution functions of the longitudinal virtual photon are derived in the leading--logarithmic approximation. It is shown that the resulting PDF satisfy the same homogeneous evolution equations as those of hadrons, but contrary to the latter are perturbatively calculable. Properties of these distribution functions are discussed and their phenomenological consequences outlined. 
Jiri Chyla