We present an updated determination of the z \sim 4 QSO luminosity function ( QLF ) , improving the quality of the determination of the faint end of the QLF presented in Glikman et al .
( 2010 ) .
We have observed an additional 43 candidates from our survey sample , yielding one additional QSO at z = 4.23 and increasing the completeness of our spectroscopic follow-up to 48 % for candidates brighter than R = 24 over our survey area of 3.76 { \mathrm { deg ^ { 2 } } } .
We study the effect of using K -corrections to compute the rest-frame absolute magnitude at 1450Ã Â compared with measuring M _ { 1450 } directly from the object spectra .
We find a luminosity-dependent bias : template-based K -corrections overestimate the luminosity of low-luminosity QSOs , likely due to their reliance on templates derived from higher luminosity QSOs .
Combining our sample with bright quasars from the Sloan Digital Sky Survey and using spectrum-based M _ { 1450 } for all the quasars , we fit a double-power-law to the binned QLF .
Our best fit has a bright-end slope , \alpha = Ð 3.3 \pm 0.2 , and faint-end slope , \beta = Ð 1.6 ^ { +0.8 } _ { -0.6 } .
Our new data revise the faint-end slope of the QLF down to flatter values similar to those measured at z \sim 3 .
The break luminosity , though poorly constrained , is at M ^ { * } = -24.1 ^ { 0.7 } _ { -1.9 } , approximately 1 - 1.5 mag fainter than at z \sim 3 .
This QLF implies that QSOs account for about half the radiation needed to ionize the IGM at these redshifts .