We present spectroscopic observations obtained with the ESO Very Large Telecope (VLT) of seven candidate Ly-alpha emitting galaxies in the field of the radio quiet Q1205-30 at z=3.04 previously detected with deep narrow band imaging. Based on equivalent widths and limits on line ratios we confirm that all seven objects are Ly-alpha emitting galaxies. Deep images also obtained with the VLT in the B and I bands show that five of the seven galaxies have very faint continuum fluxes (I(AB) approx. 26.8 and B(AB) approx. 27.3). The star formation rates of these seven galaxies estimated from the rest-frame UV continuum around 2000AA, as probed by the I-band detections, as well as from the Ly-alpha luminosities, are 1-4 M_sun yr^{-1}. This is 1-3 orders of magnitude lower than for other known populations of star-forming galaxies at similar redshifts (the Lyman-Break galaxies and the sub-mm selected sources). The inferred density of the objects is high, 16+-4 per arcmin^2 per unit redshift. This is consistent with the integrated luminosity function for Lyman-Break galaxies down to R=27 if the fraction of Ly-alpha emitting galaxies is approx. 70% at the faint end of the luminosity function. However, if this fraction is 20% as reported for the bright end of the luminosity function then the space density in this field is significantly larger (by a factor of 3.5) than expected from the luminosity function for Lyman-Break galaxies in the HDF-North. This would be an indication that at least some radio quiet QSOs at high redshift reside in overdense environments or that the faint end slope of the high redshift luminosity function has been underestimated. These observations show that Ly-alpha emission is an efficient method by which to probe the faint end of the luminosity function at high redshifts.
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