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Abstract We present the Lyαemission line luminosity function (LF) of the active galactic nuclei (AGN) in the first release of the Hobby–Eberly Telescope Dark Energy Experiment Survey (HETDEX) AGN catalog. The AGN are selected either by emission line pairs characteristic of AGN or by a single broad emission line, free of any photometric preselections (magnitude/color/morphology). The sample consists of 2346 AGN spanning 1.88 <z< 3.53, covering an effective area of 30.61 deg². Approximately 2.6% of the HETDEX AGN are not detected at >5σconfidence atr∼ 26 in the deepestr-band images we have searched. The Lyαline luminosity ranges from ∼10^42.3to 10^45.9erg s⁻¹. Our LyαLF shows a turnover luminosity with opposite slopes on the bright end and the faint end: The space density is highest at $L_{\text{Ly}\text{α}}^{\ast }={10}^{43.4}$erg s⁻¹. We explore the evolution of the AGN LF over a broader redshift range (0.8 <z< 3); constructing the rest-frame ultraviolet (UV) LF with the 1450 Å monochromatic luminosity of the power-law component of the continuum (M₁₄₅₀) fromM₁₄₅₀∼ −18 to −27.5. We divide the sample into three redshift bins (z∼ 1.5, 2.1, and 2.6). In all three redshift bins, our UV LFs indicate that the space density of AGN is highest at the turnover luminosity $M_{1450}^{*}$with opposite slopes on the bright end and the faint end. TheM₁₄₅₀LFs in the three redshift bins can be well fit with a luminosity evolution and density evolution model: the turnover luminosity ( $M_{1450}^{*}$) increases, and the turnover density (Φ*) decreases with increasing redshift. 

Abstract We present the first active galactic nuclei (AGN) catalog of the Hobby–Eberly Telescope Dark Energy Experiment Survey (HETDEX) observed between 2017 January and 2020 June. HETDEX is an ongoing spectroscopic survey (3500–5500 Å) with no target preselection based on magnitudes, colors or morphologies, enabling us to select AGN based solely on their spectral features. Both luminous quasars and low-luminosity Seyferts are found in our catalog. AGN candidates are selected with at least two significant AGN emission lines, such as the Lyαand Civλ1549 line pair, or with a single broad emission line with FWHM > 1000 km s⁻¹. Each source is further confirmed by visual inspections. This catalog contains 5322 AGN, covering an effective sky coverage of 30.61 deg². A total of 3733 of these AGN have secure redshifts, and we provide redshift estimates for the remaining 1589 single broad-line AGN with no crossmatched spectral redshifts from the Sloan Digital Sky Survey Data Release 14 of QSOs. The redshift range of the AGN catalog is 0.25 <z< 4.32, with a median ofz= 2.1. The bolometric luminosity range is 10⁹–10¹⁴L_☉with a median of 10¹²L_☉. The medianr-band magnitude of our AGN catalog is 21.6 mag, with 34% havingr> 22.5, and 2.6% reaching the detection limit atr∼ 26 mag of the deepest imaging surveys we searched. We also provide a composite spectrum of the AGN sample covering 700–4400 Å.