  Due to the fact that HI mass measurements are not available for large galaxy
samples at high redshifts, we apply a photometric estimator of the
HI-to-stellar mass ratio (M_HI/M_*) calibrated using a local Universe sample of
galaxies to a sample of galaxies at z ~ 1 in the DEEP2 survey. We use these HI
mass estimates to calculate HI mass functions (HIMFs) and cosmic HI mass
densities (Omega_HI), and to examine the correlation between star formation
rate and HI gas content, for galaxies at z ~ 1. We have estimated HI gas masses
for ~ 7,000 galaxies in the DEEP2 survey with redshifts in the range 0.75 < z <
1.4 and stellar masses M_* > 10^{10} M_solar, using a combination of the
rest-frame ultraviolet-optical colour (NUV - r) and stellar mass density (mu_*)
as a way to estimate M_HI/M_*. It is found that the high mass end of high-z HI
mass function (HIMF) is quite similar to that of the local HIMF. The lower
limit of Omega_HI,limit = 2.1 * 10^{-4} h_70^{-1}, obtained by directly
integrating the HI mass of galaxies with M_* > 10^{10} M_solar, confirms that
massive star-forming galaxies do not dominate the neutral gas at z ~ 1. We
study the evolution of the HI mass to stellar mass ratio from z ~ 1 to today
and find a steeper relation between HI gas mass fraction and stellar mass at
higher redshifts. Specifically, galaxies with M_* = 10^{11} M_solar at z ~ 1
are found to have 3 - 4 times higher neutral gas fractions than local galaxies,
while the increase is as high as 4 - 12 times at M_* = 10^{10} M_solar. The
quantity M_HI/SFR exhibits very large scatter, and the scatter increases from a
factor of 5 - 7 at z = 0 to factors close to a hundred at z = 1. This implies
that there is no relation between HI gas and star formation in high redshift
galaxies. The HI gas must be linked to cosmological gas accretion processes at
high redshifts.
