  We investigate the black hole mass function (BHMF) and Eddington ratio
distribution function (ERDF) of broad-line AGNs at z=4, based on a sample of 52
quasars with i<23.2 at 3.50 < z < 4.25 from the Hyper Suprime-Cam Subaru
Strategic Program (HSC-SSP) S16A-Wide2 dataset, and 1,462 quasars with i<20.2
in the same redshift range from the Sloan Digital Sky Survey (SDSS) DR7 quasar
catalog. Virial BH masses of quasars are estimated using the width of the CIV
1549{\AA} line and the continuum luminosity at 1350{\AA}. To obtain the
intrinsic broad-line AGN BHMF and ERDF, we correct for the incompleteness in
the low-mass and/or low-Eddington-ratio ranges caused by the flux-limited
selection. The resulting BHMF is constrained down to $\log M_{\rm
BH}/M_{\odot}\sim7.5$. In comparison with broad-line AGN BHMFs at z=2 in the
literature, we find that the number density of massive SMBHs peaks at higher
redshifts, consistent with the "down-sizing" evolutionary scenario.
Additionally, the resulting ERDF shows a negative dependence on BH mass,
suggesting more massive SMBHs tend to accrete at lower Eddington ratios at z=4.
With the derived intrinsic broad-line AGN BHMF, we also evaluate the active
fraction of broad-line AGNs among the entire SMBH population at z=4. The
resulting active fraction may suggest a positive dependence on BH mass.
Finally, we examine the time evolution of broad-line AGN BHMF between z=4 and 6
through solving the continuity equation. The results suggest that the
broad-line AGN BHMFs at z=4-6 only show evolution in their normalization, but
with no significant changes in their shape.
