We place a limit on the logarithmic slope of the luminous quasar luminosity function at z \sim 6 of \beta \ga - 3.0 ( 90 % ) using gravitational lensing constraints to build on the limit of \beta \ga - 3.3 ( 90 % ) derived from an analysis of the luminosity distribution ( Fan et al .
2003 ) .
This tight constraint is obtained by noting that of the two quasars which are lensed by foreground galaxies , neither are multiply imaged .
These observations are surprising if the luminosity function is steep because magnification bias results in an overabundance of multiply imaged relative to singly imaged lensed quasars .
Our Bayesian analysis uses the a posteriori information regarding alignments with foreground galaxies of the two lensed quasars , and provides a constraint on \beta that is nearly independent of the uncertain evolution in the lens population .
The results suggest that the bright end of the quasar luminosity function continues to flatten out to z \sim 6 , as is observed between z \sim 3 and z \sim 5 ( Fan et al .
2001 ) .
Provided that SDSS J1148-5251 at z = 6.37 is magnified by an intervening lens galaxy at z \sim 5 ( White et al .
2003 ) , we also show that the high lens redshift in this system implies a co-moving density of massive galaxies that is close to constant out to high redshift .
This is in agreement with the lack of redshift evolution in the velocity function of dark-matter halos with velocity dispersions near 200 km sec ^ { -1 } 
as predicted by the Press-Schechter formalism .
The combination of constraints on the quasar luminosity function and lens galaxy evolution are used to compute an improved estimate for the z \sim 6 multiple image lens fraction of \sim 1 - 3 \% .