The evolving slope of the stellar mass function at 0.6 <= z < 4.5 from
  deep WFC3 data
  We used Early Release Science (ERS) observations taken with the Wide Field
Camera 3 (WFC3) in the GOODS-S field to study the galaxy stellar mass function
(GSMF) at 0.6<=z<4.5. Deep WFC3 near-IR data (for Y as faint as 27.3, J and H
as faint as 27.4 AB mag at 5 sigma), as well as deep Ks (as faint as 25.5 at 5
sigma) Hawk-I band data, provide an exquisite data set with which determine in
an unprecedented way the low-mass end of the GSMF, allowing an accurate probe
of masses as low as M~7.6 10^9 Msun at z~3. Although the area used is
relatively small (~33 arcmin^2), we found generally good agreement with
previous studies on the entire mass range. Our results show that the slope of
the faint-end increases with redshift, from alpha=-1.44+/-0.03 at z~0.8 to
alpha=-1.86+/-0.16 at z~3, although indications exist that it does not steepen
further between z~3 and z~4. This result is insensitive to any uncertainty in
the M* parameter. The steepness of the GSMF faint-end solves the well-known
disagreement between the stellar mass density (SMD) and the integrated star
formation history at z>2. However, we confirm the that there appears to be an
excess of integrated star formation with respect to the SMD at z<2, by a factor
of ~2-3. Our comparison of the observations with theoretical predictions shows
that the models forecast a greater abundance of low mass galaxies, at least up
to z~3, as well as a dearth of massive galaxies at z~4 with respect to the
data, and that the predicted SMD is generally overestimated at z<~2.
