Spectrscopic CCD Surveys for Quasars at Large Redshift.IV.Evolution of the Luminosity Function from Quasars Detected by Their Lyman-Alpha Emission

We use 90 quasars detected by their Lyα emission to well-defined flux limits in the Palomar Transit Grism Survey to derive the luminosity function of quasars in the redshift range 2.75-4.75. Application of the V/V_max_ test yields (V_e_/V_a_) = 0.377+/-0.026, corresponding to a nonuniform distribution in comoving coordinates, such that the space density decreases with redshift. The luminosity function appears to be well represented by a power law with a slope corresponding to a factor of 5.6 per magnitude. We discuss and define the relationship between the line luminosity function and the continuum luminosity function of quasars. The space density for M_B_ < - 26 decreases by a factor of 2.7 per unit redshift beyond z = 2.7. Based on this result and earlier published work on quasar luminosity functions at lower redshifts, it appears that there is a maximum in the comoving space density of quasars with M_B_ < - 26 between redshifts 1.7 and 2.7.