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 \sim 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 M _ { 1450 } = -22 to -29 mag is constructed .
It is well described by a double power-law model with a knee at M _ { 1450 } = -25.36 \pm 0.13 mag and a flat faint-end slope with a power-law index of -1.30 \pm 0.05 .
The knee and faint-end slope show no clear evidence of redshift evolution from those at z \sim 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 M _ { 1450 } luminosity function to the hard X-ray 2–10 keV 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 .