The galaxy stellar mass function (GSMF) at high-z provides key information on star-formation history and mass assembly in the young Universe. We aimed to use the unique combination of deep optical/NIR/MIR imaging provided by HST, Spitzer and the VLT in the CANDELS-UDS, GOODS-South, and HUDF fields to determine the GSMF over the redshift range 3.5<z<7.5. We utilised the HST WFC3/IR NIR imaging from CANDELS and HUDF09, reaching H~27-28.5 over a total area of 369 arcmin2, in combination with associated deep HST ACS optical data, deep Spitzer IRAC imaging from the SEDS programme, and deep Y and K-band VLT Hawk-I images from the HUGS programme, to select a galaxy sample with high-quality photometric redshifts. These have been calibrated with more than 150 spectroscopic redshifts in the range 3.5<z<7.5, resulting in an overall precision of sigma_z/(1+z)~0.037. We have determined the low-mass end of the high-z GSMF with unprecedented precision, reaching down to masses as low as M*~10^9 Msun at z=4 and ~6x10^9 Msun at z=7. We find that the GSMF at 3.5<z<7.5 depends only slightly on the recipes adopted to measure the stellar masses, namely the photo-z, the SFHs, the nebular contribution or the presence of AGN on the parent sample. The low-mass end of the GSMF is steeper than has been found at lower redshifts, but appears to be unchanged over the redshift range probed here. Our results are very different from previous GSMF estimates based on converting UV galaxy luminosity functions into mass functions via tight M/L relations. Integrating our evolving GSMF over mass, we find that the growth of stellar mass density is barely consistent with the time-integral of the SFR density over cosmic time at z>4. These results confirm the unique synergy of the CANDELS+HUDF, HUGS, and SEDS surveys for the discovery and study of moderate/low-mass galaxies at high redshifts.
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