We present the analysis of a new flux-limited sample of bright quasars
and Seyfert 1 galaxies in an effective area of 611 deg(2), drawn from
the Hamburg/ESO survey. We confirm recent claims that bright quasars
have a higher surface density than previously thought. Special care wa
s taken to avoid morphological and photometric biases against low-reds
hift quasars, and about 50 % of the sample objects are at z < 0.3, spa
nning a range of Delta M similar or equal to 8 in absolute magnitudes.
While our derived space densities for low-luminosity Seyfert 1 nuclei
are consistent with those found in the literature, we find that lumin
ous QSOs, M-B < -24, are much more numerous in the local universe than
previous surveys indicated. The optical luminosity functions of Seyfe
rt 1 nuclei and QSOs join smoothly, and if the host galaxy contributio
ns are taken into account, a single power-law of slope alpha = -2.2 de
scribes the combined local luminosity function adequately, over the fu
ll range in absolute magnitude. Comparing our data with published resu
lts at higher redshifts, we can rule out pure luminosity evolution as
an acceptable parametrisation; the luminosity function of quasars chan
ges shape and slope with z, in the sense that the most luminous quasar
s show the weakest evolution.