Black-hole masses of distant quasars
  A brief overview of the methods commonly used to determine or estimate the
black hole mass in quiescent or active galaxies is presented and it is argued
that the use of mass-scaling relations is both a reliable and the preferred
method to apply to large samples of distant quasars. The method uses
spectroscopic measurements of a broad emission-line width and continuum
luminosity and currently has a statistical 1 sigma uncertainty in the absolute
mass values of about a factor of 4. Potentially, this accuracy can be improved
in the future. When applied to large samples of distant quasars it is evident
that the black hole masses are very large, of order 1 to 10 billion solar
masses, even at the highest redshifts of 4 to 6. The black holes must build up
their mass very fast in the early universe. Yet they do not grow much larger
than that: a maximum mass of about 10 billion solar masses is also observed.
Preliminary mass functions of active black holes are presented for several
quasar samples, including the Sloan Digital Sky Survey. Finally, common
concerns related to the application of the mass scaling relations, especially
for high redshift quasars, are briefly discussed.
