Exploring Reionization-era Quasars. III. Discovery of 16 Quasars at 6.4 ≲ z ≲ 6.9 with DESI Legacy Imaging Surveys and the UKIRT Hemisphere Survey and Quasar Luminosity Function at z ∼ 6.7

This is the third paper in a series aimed at finding reionization-era quasars with the combination of DESI Legacy imaging Surveys (DELS), the Pan-STARRS1 (PS1) Survey, and near-infrared imaging surveys, such as the UKIRT Hemisphere Survey (UHS), as well as the Wide-field Infrared Survey Explorer (WISE) mid-infrared survey. In this paper, we describe the updated quasar candidate selection procedure, report the discovery of 16 quasars at 6.4 ≲ z ≲ 6.9 from an area of ∼13,020 deg², and present the quasar luminosity function (QLF) at z ∼ 6.7. The measured QLF follows Φ(L₁₄₅₀)∝ L₁₄₅₀ ^-2.35 in the magnitude range-27.6 < M ₁₄₅₀ <-25.5. We determine the quasar comoving spatial density at &langle; z&rangle; = 6.7 and M ₁₄₅₀ <-26.0 to be 0.39 ± 0.11 Gpc^-3 and find the exponential density evolution parameter to be k =-0.78 ± 0.18 from z ∼ 6 to z ∼ 6.7, corresponding to a rapid decline by a factor of ∼6 per unit redshift toward earlier epochs. This indicates that the rapid decline of quasar spatial density at z > 5 that was found by previous works continues to z > 6, at a rate significantly faster than the average decline rate between z ∼ 3 and 5. We measured quasar comoving emissivity at z ∼ 6.7, which indicates that high-redshift quasars are highly unlikely to make a significant contribution to hydrogen reionization. The broad absorption line quasar fraction at z ⪆ 6.5 is measured to be ⪆22%. In addition, we also report the discovery of six additional quasars at z ∼ 6 in the Appendix.