Offset in frequency between the central UV target and the serendipitous [C II] in the same pointing. We see that the distribution is non-uniform, with several sources lying at a frequency (and hence a redshift) close to that of the central target. We thus defined two subsamples (named “clustered” and “field”, respectively) and evaluated two distinct LFs in order to account for any bias due to overdense regions. The separation between the two sample relies on the frequency width of one ALMA sideband (3.6 GHz), corresponding to a velocity separation ≷2000 km s⁻¹.