Broad-Line AGN at $3.5<z<6$: The Black Hole Mass Function and a Connection with Little Red Dots

We present a sample of 50 H-alpha detected broad-line active galactic nuclei (BLAGN) at redshifts 3.5<z<6.8 using data from the CEERS and RUBIES surveys. We select these sources directly from JWST/NIRSpec G395M/F290LP spectra. We use a multi-step pre-selection and a Bayesian fitting procedure to ensure a high-quality sample of sources with broad Balmer lines and narrow forbidden lines. We compute rest-frame ultraviolet and optical spectral slopes for these objects, and determine that 10 BLAGN in our sample are also little red dots (LRDs). These LRD BLAGN, when examined in aggregate, show broader H-alpha line profiles and a higher fraction of broad-to-narrow component H-alpha emission than non-LRD BLAGN. Moreover, we find that ~66% of these objects are intrinsically reddened (beta (optical)>0), independent of the contributions of emission lines to the broadband photometry. We construct the black hole (BH) mass function at 3.5<z<6 after computing robust observational and line detection completeness corrections. This BH mass function shows broad agreement with both recent JWST/NIRSpec and JWST/NIRCam WFSS based BH mass functions, though we extend these earlier results to log(M(BH)/M(sun)) < 7. The derived BH mass function is consistent with a variety of theoretical models, indicating that the observed abundance of black holes in the early universe is not discrepant with physically-motivated predictions. The BH mass function shape resembles a largely featureless power-law, suggesting that any signature from black-hole seeding has been lost by redshift z~5-6. Finally, we compute the BLAGN UV luminosity function and find good agreement with JWST-detected BLAGN samples from recent works, finding that BLAGN hosts constitute <10% of the total observed UV luminosity at all but the brightest luminosities.