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We present the final results from our survey of luminous $z \sim $ 5.5 quasars. This is the first systematic quasar survey focusing on quasars at $z \sim$ 5.5, during the post-reionization epoch. It has been challenging to select quasars at $5.3 < z < 5.7$ using conventional color selections, due to their similar optical colors to those of late-type stars, especially M dwarfs. We developed a new selection technique for $z \sim$ 5.5 quasars based on optical, near-IR, and mid-IR photometry, using data from the Sloan Digital Sky Survey (SDSS), PanSTARR1 (PS1), the UKIRT Infrared Deep Sky Surveys - Large Area Survey, the UKIRT Hemisphere Survey, the VISTA Hemisphere Survey, and the Wide Field Infrared Survey Explorer ($WISE$), covering $\sim$ 11000 deg$^2$ of high galactic latitude sky. In this paper, we present the discovery of 15 new quasars at $z\sim 5.5$. Together with results from Yang et al. (2017), our survey provides a complete, flux-limited sample of 31 quasars at $5.3 \le z \le 5.7$. We measure the quasar spatial density at $z \sim 5.5$ and $M_{1450} < -26.2$. Our result is consistent with the rapid decline of quasar spatial density from $z = 5$ to 6, with $k=-0.66 \pm 0.05$ ($\rho(z) \propto 10^{kz}$). In addition, we present a new survey using optical colors only from the full PS1 area for luminous quasars at $z = 5.0 - 5.5$, beyond the SDSS footprint, and report the preliminary results from this survey, including 51 new quasars discovered at $4.61\le z \le5.71$.

Filling in the Quasar Redshift Gap at z ∼ 5.5. II. A Complete Survey of Luminous Quasars in the Post-reionization Universe