Luminosity function of quasars at $1.0<z<3.5$ from SDSS and DESI

We present a study of the evolution of type 1 quasars at $1.0<z<3.5$, covering the peak epoch of quasar activity. The quasar evolution has been extensively explored by a variety of previous works and the derived quasar luminosity functions (QLFs) are not well consistent with each other, presumably due to the complexities introduced by different quasar selection techniques and associated completeness corrections. We use a new strategy to construct QLFs based on a library of all known quasars. We focus on a wide region of $\sim$1700 deg$^2$ and a deep field of $\sim$265 deg$^2$ that have rich spectroscopic data primarily from SDSS and DESI. We then apply traditional color cuts in the rest-frame UV/optical to select quasar candidates and use the quasar library to identify them. Our final sample consists of 62,426 quasars at $1.0<z<3.5$, with a high completeness ($\sim$96%) and a high purity ($\sim$93%) in the color selection. Simple color cuts can potentially minimize selection biases for the study of quasar evolution. We derive binned QLFs and characterize them using a double power-law model. Sample incompleteness and contamination are considered as part of the uncertainties in the calculation. Compared to previous results, our QLFs are slightly higher at the faint end, and also higher at the bright end at $2.5<z<3.5$. The QLFs suggest that the quasar evolution at $1.0 < z < 2.5$ can be well described by the pure luminosity evolution model, while at $2.5 < z < 3.5$, it can be described by either the pure luminosity evolution or the pure density evolution model.