Clustering of quasars in a wide luminosity range at redshift 4 with
  Subaru Hyper Suprime-Cam wide field imaging
  We examine the clustering of quasars over a wide luminosity range, by
utilizing 901 quasars at $\overline{z}_{\rm phot}\sim3.8$ with $-24.73<M_{\rm
1450}<-22.23$ photometrically selected from the Hyper Suprime-Cam Subaru
Strategic Program (HSC-SSP) S16A Wide2 date release and 342 more luminous
quasars at $3.4<z_{\rm spec}<4.6$ having $-28.0<M_{\rm 1450}<-23.95$ from the
Sloan Digital Sky Survey (SDSS) that fall in the HSC survey fields. We measure
the bias factors of two quasar samples by evaluating the cross-correlation
functions (CCFs) between the quasar samples and 25790 bright $z\sim4$ Lyman
Break Galaxies (LBGs) in $M_{\rm 1450}<-21.25$ photometrically selected from
the HSC dataset. Over an angular scale of \timeform{10.0"} to
\timeform{1000.0"}, the bias factors are $5.93^{+1.34}_{-1.43}$ and
$2.73^{+2.44}_{-2.55}$ for the low and high luminosity quasars, respectively,
indicating no luminosity dependence of quasar clustering at $z\sim4$. It is
noted that the bias factor of the luminous quasars estimated by the CCF is
smaller than that estimated by the auto-correlation function (ACF) over a
similar redshift range, especially on scales below \timeform{40.0"}. Moreover,
the bias factor of the less-luminous quasars implies the minimal mass of their
host dark matter halos (DMHs) is $0.3$-$2\times10^{12}h^{-1}M_{\odot}$,
corresponding to a quasar duty cycle of $0.001$-$0.06$.
