A Snapshot Survey for Gravitational Lenses among z>=4.0 Quasars. II. Constraints on the 4.0

We report on i-band snapshot observations of 157 Sloan Digital SkySurvey quasars at 4.0-3.8 (3 σ), assuming a break in the quasar luminosityfunction at M^*₁₄₅₀~-24.5. This constraint isconsiderably stronger than the limit of β>-4.63 obtained fromthe absence of lensing in four z>5.7 quasars. Such constraints areimportant to our understanding of the true space density ofhigh-redshift quasars and the ionization state of the early universe.Based on observations made with the NASA/ESA Hubble Space Telescope,obtained at the Space Telescope Science Institute, which is operated bythe Association of Universities for Research in Astronomy, Inc., underNASA contract NAS5-26555. These observations are associated with program9472.