The Quasar Luminosity Function at Redshift 4 with Hyper Suprime-Cam Wide
  Survey
  We present the luminosity function of z=4 quasars based on the Hyper
Suprime-Cam Subaru Strategic Program Wide layer imaging data in the g, r, i, z,
and y bands covering 339.8 deg^2. From stellar objects, 1666 z~4 quasar
candidates are selected by the g-dropout selection down to i=24.0 mag. Their
photometric redshifts cover the redshift range between 3.6 and 4.3 with an
average of 3.9. In combination with the quasar sample from the Sloan Digital
Sky Survey in the same redshift range, the quasar luminosity function covering
the wide luminosity range of M1450=-22 to -29 mag is constructed. It is well
described by a double power-law model with a knee at M1450=-25.36+-0.13 mag and
a flat faint-end slope with a power-law index of -1.30+-0.05. The knee and
faint-end slope show no clear evidence of redshift evolution from those at z~2.
The flat slope implies that the UV luminosity density of the quasar population
is dominated by the quasars around the knee, and does not support the steeper
faint-end slope at higher redshifts reported at z>5. If we convert the M1450
luminosity function to the hard X-ray 2-10keV luminosity function using the
relation between UV and X-ray luminosity of quasars and its scatter, the number
density of UV-selected quasars matches well with that of the X-ray-selected
AGNs above the knee of the luminosity function. Below the knee, the UV-selected
quasars show a deficiency compared to the hard X-ray luminosity function. The
deficiency can be explained by the lack of obscured AGNs among the UV-selected
quasars.
