  The leptogenesis is studied in the neutrino mass matrix with two zeros, which
reduces the number of independent phases of the CP violation. These texture
zeros are decomposed into the Dirac neutrino mass matrix and the right-handed
Majorana one in the see-saw mechanism. It is found that there are six textures
for the Dirac neutrino mass matrix, among which one texture with three zeros
has three phases, three textures with four zeros have two phases, and two
textures with five zeros have only one phase in the basis with the real
right-handed Majorana mass matrix. The relation between the leptogenesis and
the low energy CP violation is discussed in typical textures. It is remarked
that the leptogenesis is linked strongly with the CP violation in the neutrino
oscillations. The predicted baryon asymmetry of the universe is consistent with
the observed value.
