Spectroscopic 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.