  We have analysed the optical luminosity-redshift distribution properties of
bright QSOs, using a new large sample from the Hamburg/ESO survey. The sample
provides insight into the hitherto poorly sampled bright tail of the luminosity
function, allowing to monitor its evolution with redshift up to $z\approx 3$.
The slope increases significantly towards higher $z$, inconsistent with the
predictions of pure luminosity evolution, but also with other recently proposed
parameterisations. This phenomenon is opposite to what would be expected from
gravitational lensing, showing that magnification bias does not significantly
distort the QSO luminosity function within the redshift range covered. The
space density of high-luminosity QSOs continues to increase up to the
high-redshift limit of the survey, without indication of reduced evolution
above $z\simeq 2$. The sample also permits an improved estimate of the local
($z\approx 0$) luminosity function of QSOs and bright Seyfert~1 nuclei, over
the luminosity range $-27\la M_{B_J}\la -20$. No evidence for a break or change
of slope is found down to absolute magnitudes $M_{B_J}\simeq-20$.
