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We apply a simple statistical method (Derenzo & Hildebrand 1969) to estimating the completeness of quasar surveys. It requires that an area has been covered by two or more, preferably different, selection techniques. We use three suitable data sets with separate selections from: variability and UV-excess (170 quasars); objective prism and UV-excess (141 quasars); multicolour and X-ray ({it ROSAT,} 19 quasars). We find that, for selection by UV-excess, the common limit of $U-B le -0.35 pm -0.05$ leads to losses of $sim 35%$, typically missing low-luminosity $(M_{B} gtrsim -24.5)$ quasars, independently of redshift. Systematic incompleteness will therefore affect the new generation of large quasar surveys that select by $U-B le -0.35$. By correcting for this incompleteness, we find, from the first data set ($B < 21.0$ and $z < 2.2$), that the evolution of the quasar luminosity function (LF) is best described by joint luminosity and density evolution. When extrapolated to $z = 0$, the LF matches that of local Seyfert galaxies better than any previous determination. The LF shows an increase in the number of low-luminosity quasars at low redshifts and of brighter quasars at intermediate redshifts, relative to the LF of Boyle et al. (1990). This result is consistent with models in which quasars fade from an initial bright phase.
We propose a new interpretation of the quasar luminosity function (LF), derived from physically motivated models of quasar lifetimes and light curves. In our picture, quasars evolve rapidly and their lifetime depends on both their instantaneous and p
We present observations of an optically-faint quasar, RD J114816.2+525339, discovered from deep multi-color observations of the field around the z = 6.42 quasar SDSS J1148+5251. The two quasars have a projected separation of 109 arcsec and both are o
We present an updated determination of the z ~ 4 QSO luminosity function (QLF), improving the quality of the determination of the faint end of the QLF presented in Glikman et al. (2010). We have observed an additional 43 candidates from our survey sa
We introduce a method to relate a possible truncation of the star cluster mass function at the high mass end to the shape of the cluster luminosity function (LF). We compare the observed LFs of five galaxies containing young star clusters with synthe
Quasar luminosity functions are a fundamental probe of the growth and evolution of supermassive black holes. Measuring the intrinsic luminosity function is difficult in practice, due to a multitude of observational and systematic effects. As sample s