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The Infrared Medium-deep Survey. IX. Discovery of Two New $z\sim6$ Quasars and Space Density down to $M_{1450}\sim-23.5$ mag

We present the result of the Infrared Medium-deep Survey (IMS) $z\sim6$ quasar survey, using the combination of the IMS near-infrared images and the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) optical images. The traditional color-selection method results in 25 quasar candidates over $86$ deg$^{2}$. We introduce the corrected Akaike Information Criterion (AICc) with the high-redshift quasar and late-type star models to prioritize the candidates efficiently. Among the color-selected candidates, seven plausible candidates finally passed the AICc selection of which three are known quasars at $z\sim6$. The follow-up spectroscopic observations for the remaining four candidates were carried out, and we confirmed that two out of four are $z\sim6$ quasars. With this complete sample, we revisited the quasar space density at $z\sim6$ down to $M_{1450}\sim-23.5$ mag. Our result supports the low quasar space density at the luminosity where the quasar's ultraviolet ionizing emissivity peaks, favoring a minor contribution of quasars to the cosmic reionization.