We investigate the properties of ∼7000 narrow-band selected galaxies with strong Hβ+[O iii] and [O ii] nebular emission lines from the High-z Emission-Line Survey between z ∼ 0.8 and 5.0. Our sample covers a wide range in stellar mass (Mstellar ∼ 107.5–12.0 M), rest-frame equivalent widths (EWrest∼10–105 Å), and line luminosities (Lline ∼ 1040.5–43.2 erg s−1). We measure the Hβ+[O iii]-selected stellar mass functions out to z ∼ 3.5 and find that both M and ϕ increases with cosmic time. The [O ii]-selected stellar mass functions show a constant M ≈ 1011.6 M and a strong, increasing evolution with cosmic time in ϕ in line with Hα studies. We also investigate the evolution of the EWrest as a function of redshift with a fixed mass range (109.5–10.0 M) and find an increasing trend best represented by (1 + z)3.81 ± 0.14 and (1 + z)2.72 ± 0.19 up to z ∼ 2 and ∼3 for Hβ+[O iii] and [O ii] emitters, respectively. This is the first time that the EWrest evolution has been directly measured for Hβ+[O iii] and [O ii] emitters up to these redshifts. There is evidence for a slower evolution for z > 2 in the Hβ+[O iii] EWrest and a decreasing trend for z > 3 in the [O ii] EWrest evolution, which would imply low [O ii] EW at the highest redshifts and higher [O iii]/[O ii] line ratios. This suggests that the ionization parameter at higher redshift may be significantly higher than the local Universe. Our results set the stage for future near-IR space-based spectroscopic surveys to test our extrapolated predictions and also produce z > 5 measurements to constrain the high-z end of the EWrest and [O iii]/[O ii] evolution.

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