The Extremely Luminous Quasar Survey (ELQS) in the Sloan Digital Sky Survey footprint. II. The North Galactic Cap Sample.

We present the North Galactic Cap sample of the Extremely Luminous Quasar Survey (ELQS-N), which targets quasars with $M_{1450} 70\%$ over $z\sim3.0-5.0$ at $m_{i}\lesssim17.5$, 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 $6.5\,\rm{m}$ 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 $\sim79\%$. 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.