  The faint end of the differential galaxy number counts, n(m), in the Hubble
Deep Field (HDF) North has been determined for the F450W, F606W, and F814W
filters by means of surface-brightness fluctuation (SBF) measurements. This
technique allows us to explore n(m) beyond the limiting magnitude of the HDF,
providing new, stronger constraints on the faint end of n(m). This has allowed
us to test the validity of previous number count studies and to produce a new
determination of the faint end of n(m) for magnitudes fainter than 28.8 in the
AB system and to extend this estimate down to 31. This value represents an
extension of more than two magnitudes beyond the limits of previous photometric
studies. The obtained n(m) slopes are \gamma=0.27, 0.21, and 0.26 in B_{450},
V_{606}, and I_{814}, respectively.
