Euclid preparation. XIV. C3R2 survey DR3

The primary goal is to enable sufficiently accurate photometric redshifts for Stage IV dark energy projects, particularly Euclid and the Nancy Grace Roman Space Telescope (Roman), which are designed to constrain cosmological parameters through weak lensing.

We present 676 new high-confidence spectroscopic redshifts obtained by the C3R2 survey in the 2017B-2019B semesters using the DEIMOS, LRIS, and MOSFIRE multiobject spectrographs on the Keck telescopes. Combined with the 4454 redshifts previously published by this project, the C3R2 survey has now obtained and published 5130 high-quality galaxy spectra and redshifts. If we restrict consideration to only the 0.2<z_p_<2.6 range of interest for the Euclid cosmological goals, then with the current data release, C3R2 has increased the spectroscopic redshift coverage of the Euclid color space from 51% (as reported by Masters+ 2017, J/ApJ/841/111) to the current 91%.