We present the North Galactic Cap sample of the Extremely Luminous Quasar Survey ( ELQS-N ) , which targets quasars with M _ { 1450 } < -27 at 2.8 \leq z < 5 in an area of \sim 7600 deg ^ { 2 } of the Sloan Digital Sky Survey ( SDSS ) footprint with 90 \text { \textdegree } < RA < 270 \text { \textdegree } .
Based on a near-infrared/infrared JKW2 color cut , the ELQS selection efficiently uses random forest methods to classify quasars and to estimate photometric redshifts ; this scheme overcomes some of the difficulties of pure optical quasar selection at z \approx 3 .
As a result , we retain a completeness of > 70 \% over z \sim 3.0 - 5.0 at m _ { i } \lesssim 17.5 , limited toward fainter magnitudes by the depth of the Two Micron All Sky Survey ( 2MASS ) .
The presented quasar catalog consists of a total of 270 objects , of which 39 are newly identified in this work with spectroscopy obtained at the Vatican Advanced Technology Telescope and the MMT 6.5 m telescope .
In addition to the high completeness , which allowed us to discover new quasars in the already well-surveyed SDSS North Galactic Cap , the efficiency of our selection is relatively high at \sim 79 \% .
Using 120 objects of this quasar sample we are able to extend the previously measured optical quasar luminosity function ( QLF ) by one magnitude toward the bright end at 2.8 \leq z \leq 4.5 .
A first analysis of the QLF suggests a relatively steep bright-end slope of \beta \approx - 4 for this sample .
This result contrasts with previous results in the same redshift range , which find a much flatter slope around \beta \sim - 2.5 , but agrees with recent measurements of the bright-end slope at lower and higher redshifts .
Our results constrain the bright-end slope at z = 2.8 - 4.5 to \beta < -2.94 with a 99 % confidence .