A Snapshot Survey for Gravitational Lenses Among z>=4.0 Quasars: II.   Constraints on the 4.0<z<4.5 Quasar Population
  We report on i-band snapshot observations of 157 Sloan Digital Sky Survey (SDSS) quasars at 4<z<5.4 using the Advanced Camera for Surveys on the Hubble Space Telescope (HST) to search for evidence of gravitational lensing of these sources. None of the quasars appear to be strongly lensed and multiply imaged at the angular resolution (~0.1") and sensitivity of HST. The non-detection of strong lensing in these systems constrains the z=4-5 luminosity function to an intrinsic slope of beta>-3.8 (3 sigma), assuming a break in the quasar luminosity function at M_1450^star=-24.5. This constraint is considerably stronger than the limit of beta>-4.63 obtained from the absence of lensing in four z>5.7 quasars. Such constraints are important for our understanding of the true space density of high-redshift quasars and the ionization state of the early universe. 
Gordon T. Richards, Zoltan Haiman, Bartosz Pindor, Michael A. Strauss,   Xiaohui Fan, Daniel Eisenstein, Donald P. Schneider...