A Deep Survey of HI-Selected Galaxies: The HI Mass Function

We analyze the distribution of galaxy HI masses detected in a large, deep HI survey conducted at the Arecibo observatory, and we find possible evidence of a faint-end steepening of the mass function similar to what has been found optically. This is the first HI survey with enough dynamic range to see this steepening; the results of an earlier survey are found to be consistent when the detection statistics are re-examined. We demonstrate a technique for testing and correcting source count completeness in HI surveys based on the V/V_max test and the large scale structure in the regions surveyed.