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Abstract We present Ly α and ultraviolet (UV)-continuum luminosity functions (LFs) of galaxies and active galactic nuclei (AGNs) at z = 2.0–3.5 determined by the untargeted optical spectroscopic survey of the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX). We combine deep Subaru imaging with HETDEX spectra resulting in 11.4 deg 2 of fiber spectra sky coverage, obtaining 18,320 galaxies spectroscopically identified with Ly α emission, 2126 of which host type 1 AGNs showing broad (FWHM > 1000 km s −1 ) Ly α emission lines. We derive the Ly α (UV) LF over 2 orders of magnitude covering bright galaxies and AGNs in log L Ly α / [ erg s − 1 ] = 43.3 – 45.5 (−27 < M UV < −20) by the 1/ V max estimator. Our results reveal that the bright-end hump of the Ly α LF is composed of type 1 AGNs. In conjunction with previous spectroscopic results at the faint end, we measure a slope of the best-fit Schechter function to be α Sch = − 1.70 − 0.14 + 0.13 , which indicates that α Sch steepens from z = 2–3 toward high redshift. Our UV LF agrees well with previous AGN UV LFs and extends to faint-AGN and bright-galaxy regimes. The number fraction of Ly α -emitting objects ( X LAE ) increases from M UV * ∼ − 21 to bright magnitude due to the contribution of type 1 AGNs, while previous studies claim that X Ly α decreases from faint magnitudes to M UV * , suggesting a valley in the X Ly α –magnitude relation at M UV * . Comparing our UV LF of type 1 AGNs at z = 2–3 with those at z = 0, we find that the number density of faint ( M UV > −21) type 1 AGNs increases from z ∼ 2 to 0, as opposed to the evolution of bright ( M UV < −21) type 1 AGNs, suggesting AGN downsizing in the rest-frame UV luminosity. 

We describe the survey design, calibration, commissioning, and emission-line detection algorithms for the Hobby–Eberly Telescope Dark Energy Experiment (HETDEX). The goal of HETDEX is to measure the redshifts of over a million Lyαemitting galaxies between 1.88 <z< 3.52, in a 540 deg²area encompassing a comoving volume of 10.9 Gpc³. No preselection of targets is involved; instead the HETDEX measurements are accomplished via a spectroscopic survey using a suite of wide-field integral field units distributed over the focal plane of the telescope. This survey measures the Hubble expansion parameter and angular diameter distance, with a final expected accuracy of better than 1%. We detail the project’s observational strategy, reduction pipeline, source detection, and catalog generation, and present initial results for science verification in the Cosmological Evolution Survey, Extended Groth Strip, and Great Observatories Origins Deep Survey North fields. We demonstrate that our data reach the required specifications in throughput, astrometric accuracy, flux limit, and object detection, with the end products being a catalog of emission-line sources, their object classifications, and flux-calibrated spectra.