  We study the LF of the high-z galaxy population with 3<z<4 using a purely
I-band magnitude-selected spectroscopic sample obtained in the framework of the
VVDS. We determine the LF from the VVDS, taking care to add as few assumptions
and as simple corrections as possible, and compare our results with those
obtained from photometric studies, based on Lyman-break selections or photo-z
measurements. We find that in the range 3<z<4, the VVDS LF is parameterized by
phi*=1.24+-0.50 10-3 mag-1 Mpc-3 and M*=-21.49+-0.19, assuming a slope
alpha=-1.4 consistent with most previous studies. While phi* is comparable to
previously found values, M* is significantly brighter by about 0.5 mag at
least. Using the conservative slope -1.4, we find a LD at 1700A
rho(M<-18.5)=2.4 10 19 W Mpc-3 and rho Tot=3.1 10 19 W Mpc-3, comparable to
that estimated in other studies. The unexpectedly large number of very bright
galaxies found in the VVDS indicates that the color-selection and photo-z
techniques that are generally used to build high-z galaxy samples may be
affected by a significant fraction of color-measurement failures or by
incomplete modelling of the mix of stellar emission, AGN contribution, dust
absorption and intergalactic extinction assumed to identify high-z galaxies,
making pure magnitude selection better able to trace the full population.
Because of the difficulty to identify all low-luminosity galaxies in a
spectroscopic survey, the LD could still be significantly underestimated. We
also find that the relative contribution of the most luminous galaxies compared
to the fainter ones is at least twice as large in the VVDS compared to former
estimates. Therefore, the VVDS paints a quite different picture of the role of
the most actively star-forming galaxies in the history of star formation.
