Constraints on the faint end of the quasar luminosity function at z~5 in
  the COSMOS field
  We present the result of our low-luminosity quasar survey in the redshift
range of 4.5 < z < 5.5 in the COSMOS field. Using the COSMOS photometric
catalog, we selected 15 quasar candidates with 22 < i' < 24 at z~5, that are ~
3 mag fainter than the SDSS quasars in the same redshift range. We obtained
optical spectra for 14 of the 15 candidates using FOCAS on the Subaru Telescope
and did not identify any low-luminosity type-1 quasars at z~5 while a
low-luminosity type-2 quasar at z~5.07 was discovered. In order to constrain
the faint end of the quasar luminosity function at z~5, we calculated the
1sigma confidence upper limits of the space density of type-1 quasars. As a
result, the 1sigma confidence upper limits on the quasar space density are Phi<
1.33*10^{-7} Mpc^{-3} mag^{-1} for -24.52 < M_{1450} < -23.52 and Phi<
2.88*10^{-7} Mpc^{-3} mag^{-1} for -23.52 < M_{1450} < -22.52. The inferred
1sigma confidence upper limits of the space density are then used to provide
constrains on the faint-end slope and the break absolute magnitude of the
quasar luminosity function at z~5. We find that the quasar space density
decreases gradually as a function of redshift at low luminosity (M_{1450} ~
-23), being similar to the trend found for quasars with high luminosity
(M_{1450}<-26). This result is consistent with the so-called downsizing
evolution of quasars seen at lower redshifts.
