A large, deep 3 deg$^2$ survey of H$\alpha$, [OIII], and [OII] emitters
  from LAGER: constraining luminosity functions
  We present our measurements of the H$\alpha$, [OIII], and [OII] luminosity
functions as part of the Lyman Alpha Galaxies at Epoch of Reionization (LAGER)
survey using our samples of 1577 $z = 0.47$ H$\alpha$-, 3933 $z = 0.93$
[OIII]-, and 5367 $z = 1.59$ [OII]-selected emission line galaxies in a single
3 deg$^2$ CTIO/Blanco DECam pointing of the COSMOS field. Our observations
reach 5$\sigma$ depths of $8.2\times10^{-18}$ erg s$^{-1}$ cm$^{-2}$ and
comoving volumes of $(1-7)\times10^{5}$ Mpc$^3$ making our survey one of the
deepest narrowband surveys. We measure the observed luminosity functions and
find best-fits of $\phi^\star = 10^{-3.16\pm0.09}$ Mpc$^{-3}$ and $L^\star =
10^{41.72\pm0.09}$ erg s$^{-1}$ for H$\alpha$, $\phi^\star =
10^{-2.16^{+0.10}_{-0.12}}$ Mpc$^{-3}$ and $L^\star =
10^{41.38^{+0.07}_{-0.06}}$ erg s$^{-1}$ for [OIII], and $\phi^\star =
10^{-1.97^{+0.07}_{-0.07}}$ Mpc$^{-3}$ and $L^\star = 10^{41.66\pm0.03}$ erg
s$^{-1}$ for [OII], with $\alpha$ fixed to $-1.75$, $-1.6$, and $-1.3$,
respectively. An excess of bright $> 10^{42}$ erg s$^{-1}$ [OIII] emitters is
observed and may be due to AGN contamination. Dust corrections are applied
assuming $A_{\rm{H}\alpha} = 1$ mag. We also design our own empirical
rest-frame $g - r$ calibration using SDSS DR12 data, test it against our $z =
0.47$ H$\alpha$ emitters with $z$COSMOS $1$D spectra, and calibrate it for $(g
- r)$ between $-0.8$ and $1.3$ mag. Dust and AGN-corrected star formation rate
densities (SFRDs) are measured as $\log_{10}\rho_{\rm{SFR}}/(\rm{M}_\odot\
\rm{yr}^{-1}\ \rm{Mpc}^{-3}) = -1.63\pm0.04$, $-1.07\pm0.06$, and
$-0.90\pm0.10$ for H$\alpha$, [OIII], and [OII], respectively. We find our
[OIII] and [OII] samples fully trace cosmic star formation activity at their
respective redshifts in comparison to multi-wavelength SFRDs, while the
H$\alpha$ sample traces $\sim 70$ percent of the total $z = 0.47$ SFRD.
