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A Steep Faint-End Slope of the UV Luminosity Function at z~2-3: Implications for the Global Stellar Mass Density and Star Formation in Low Mass Halos

We use the deep ground-based optical photometry of the Lyman Break Galaxy (LBG) Survey to derive robust measurements of the faint-end slope (alpha) of the UV LF at redshifts 1.9<z<3.4. Our sample includes >2000 spectroscopic redshifts and ~31000 LBGs in 31 spatially-independent fields over a total area of 3261 arcmin^2. These data allow us to select galaxies to 0.07L* and 0.10L* at z~2 and z~3, respectively. A maximum likelihood analysis indicates steep values of alpha(z=2)=-1.73+/-0.07 and alpha(z=3)=-1.73+/-0.13. This result is robust to luminosity dependent systematics in the Ly-alpha equivalent width and reddening distributions, is similar to the steep values advocated at z>4, and implies that ~93% of the unobscured UV luminosity density at z~2-3 arises from sub-L* galaxies. With a realistic luminosity dependent reddening distribution, faint to moderately luminous galaxies account for >70% and >25% of the bolometric luminosity density and present-day stellar mass density, respectively, when integrated over 1.9<z<3.4. We find a factor of 8-9 increase in the star formation rate density between z~6 and z~2, due to both a brightening of L* and an increasing dust correction proceeding to lower redshifts. The previously observed discrepancy between the integral of the star formation history and stellar mass density measurements at z~2 may be reconciled by invoking a luminosity dependent reddening correction to the star formation history combined with an accounting for the stellar mass contributed by UV-faint galaxies. The steep and relatively constant alpha of the UV LF at z>2 contrasts with the shallower value inferred locally, suggesting that the evolution in the faint-end slope may be dictated simply by the availability of low mass halos capable of supporting star formation at z<2. [Abridged]