The Arecibo Galaxy Environments survey IV: the NGC7448 region and the HI
  mass function
  In this paper we describe results from the Arecibo Galaxy Environments Survey
(AGES). The survey reaches column densities of ~3x10^18 cm^-2 and masses of
~10^7 M_O, over individual regions of order 10 sq deg in size, out to a maximum
velocity of 18,000 km s^-1. Each surveyed region is centred on a nearby galaxy,
group or cluster, in this instance the NGC7448 group. Galaxy interactions in
the NGC7448 group reveal themselves through the identification of tidal tails
and bridges. We find ~2.5 times more atomic gas in the inter-galactic medium
than in the group galaxies. We identify five new dwarf galaxies, two of which
appear to be members of the NGC7448 group. This is too few, by roughly an order
of magnitude, dwarf galaxies to reconcile observation with theoretical
predictions of galaxy formation models. If they had observed this region of sky
previous wide area blind HI surveys, HIPASS and ALFALFA, would have detected
only 5% and 43% respectively of the galaxies we detect, missing a large
fraction of the atomic gas in this volume. We combine the data from this paper
with that from our other AGES papers (370 galaxies) to derive a HI mass
function with the following Schechter function parameters alpha=-1.52+/-0.05,
M^*=5.1+/-0.3x10^9 h_72^-2 M_O, phi=8.6+/-1.1x10-3 h_72^3 Mpc^-3 dex-1.
Integrating the mass function leads to a cosmic mass density of atomic hydrogen
of Omega_HI=5.3+/-0.8x10^-4 h_72^-1. Our mass function is steeper than that
found by both HIPASS and ALFALFA (alpha=1.37 and 1.33 respectively), while our
cosmic mass density is consistent with ALFALFA, but 1.7 times larger than found
by HIPASS.
