  We present the analysis of a new flux-limited sample of bright quasars and
Seyfert 1 galaxies in an effective area of 611 square deg, drawn from the
Hamburg/ESO survey. We confirm recent claims that bright quasars have a higher
surface density than previously thought. Special care was taken to avoid
morphological and photometric biases against low-redshift quasars, and about 50
% of the sample objects are at z < 0.3, spanning a range of three decades in
luminosity. While our derived space densities for low-luminosity Seyfert 1
nuclei are consistent with those found in the literature, we find that luminous
QSOs, M_B < -24, are much more numerous in the local universe than previous
surveys indicated. The optical luminosity functions of Seyfert 1 nuclei and
QSOs join smoothly, and if the host galaxy contributions are taken into
account, a single power-law of slope alpha = -2.2 describes the combined local
luminosity function adequately, over the full range in absolute magnitude.
Comparing our data with published results at higher redshifts, we can rule out
pure luminosity evolution as an acceptable parametrisation; the luminosity
function of quasars changes shape and slope with z, in the sense that the most
luminous quasars show the weakest evolution.
