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We present the luminosity function of z=4 quasars based on the HyperSuprime-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 quasarcandidates are selected by the g-dropout selection down to i=24.0 mag. Theirphotometric redshifts cover the redshift range between 3.6 and 4.3 with anaverage of 3.9. In combination with the quasar sample from the Sloan DigitalSky Survey in the same redshift range, the quasar luminosity function coveringthe wide luminosity range of M1450=-22 to -29 mag is constructed. It is welldescribed by a double power-law model with a knee at M1450=-25.36+-0.13 mag anda flat faint-end slope with a power-law index of -1.30+-0.05. The knee andfaint-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 populationis dominated by the quasars around the knee, and does not support the steeperfaint-end slope at higher redshifts reported at z>5. If we convert the M1450luminosity function to the hard X-ray 2-10keV luminosity function using therelation between UV and X-ray luminosity of quasars and its scatter, the numberdensity of UV-selected quasars matches well with that of the X-ray-selectedAGNs above the knee of the luminosity function. Below the knee, the UV-selectedquasars show a deficiency compared to the hard X-ray luminosity function. Thedeficiency can be explained by the lack of obscured AGNs among the UV-selectedquasars.

The Quasar Luminosity Function at Redshift 4 with Hyper Suprime-Cam Wide Survey