Over the last few years , the Sloan Digital Sky Survey ( SDSS ) has discovered several hundred quasars with redshift between 4.0 and 6.4 .
Including the effects of magnification bias , one expects a priori that an appreciable fraction of these objects are gravitationally lensed .
We have used the Advanced Camera for Surveys on the Hubble Space Telescope to carry out a snapshot imaging survey of high-redshift SDSS quasars to search for gravitationally split lenses .
This paper , the first in a series reporting the results of the survey , describes snapshot observations of four quasars at z = 5.74 , 5.82 , 5.99 and 6.30 , respectively .
We find that none of these objects has a lensed companion within 5 magnitudes with a separation larger than 0.3 
arcseconds ; within 2.5 magnitudes , we can rule out companions within 0.1 arcseconds .
Based on the non-detection of strong lensing in these four systems , we constrain the z \sim 6 luminosity function to a slope of \beta > -4.63 ( 3 \sigma ) , assuming a break in the quasar luminosity function at M _ { 1450 } ^ { \star } = -24.0 .
We discuss the implications of this constraint on the ionizing background due to quasars in the early universe .
Given that these quasars are not highly magnified , estimates of the masses of their central engines by the Eddington argument must be taken seriously , possibly challenging models of black hole formation .