Ultra-luminous high-redshift quasars from SkyMapper -- II. New quasars
  and the bright end of the luminosity function
  We search for ultra-luminous Quasi-Stellar Objects (QSOs) at high redshift
using photometry from the SkyMapper Southern Survey Data Release 3 (DR3), in
combination with 2MASS, VHS DR6, VIKING DR5, AllWISE, and CatWISE2020, as well
as parallaxes and proper motions from Gaia DR2 and eDR3. We report 142 newly
discovered Southern QSOs at $3.8<z<5.5$, of which 126 have $M_{145} <-27$ ABmag
and are found in a search area of 14,486 deg$^2$. This Southern sample,
utilising the Gaia astrometry to offset wider photometric colour criteria,
achieves unprecedented completeness for an ultra-luminous QSO search at high
redshift. In combination with already known QSOs, we construct a sample that is
$>80$ per cent complete for $M_{145}<-27.33$ ABmag at $z=4.7$ and for
$M_{145}<-27.73$ ABmag at $z=5.4$. We derive the bright end of the QSO
luminosity function at restframe 145 nm for $z=4.7-5.4$ and measure its slope
to be $\beta = -3.60\pm0.37$ and $\beta = -3.38\pm0.32$ for two different
estimates of the faint-end QSO density adopted from the literature. We also
present the first $z\sim 5$ QSO luminosity function at restframe 300 nm.
