We present the results of deep Lyman limit imaging in four new elds as part of a continuing search for galaxies at 3:0 z 3:5. The technique uses a custom broad{band lter set (U n GR) designed to isolate objects having Lyman continuum breaks superposed on otherwise at{spectrum ultraviolet continua. The observations are speci cally aimed at detecting known galaxies producing optically thick QSO metal line absorption systems, but are equally sensitive to more generally distributed objects at the redshifts of interest.We have identi ed a plausible candidate for the QSO absorber in one out of the four new elds surveyed; in the other three the absorbing galaxy must be either fainter than R = 25:5 or closer than 1 arcsec to the QSO sight-line (or both). Together with previously published results of the survey, we have now detected in two out of six cases objects with the expected properties of star{forming galaxies at z > 3 within 3 arcsec of the QSO sight lines; the two candidate absorbers have similar luminosities, M B ' 22 (q 0 = 0:5, H 0 = 50 km s 1 Mpc 1 ), and impact parameters, R 10 h 1 kpc.We nd the average surface density of robust Lyman break objects to be 0:5 galaxies per square arcminute to a magnitude limit R = 25:0 . A simple, \no evolution" model based on the properties of normal galaxies at z < 1 predicts a density of Lyman break objects only a few times larger than observed. We conclude that there is a substantial population of star{forming galaxies, of relatively normal luminosity, already 1 Alfred P. Sloan Foundation Fellow 2 NSF Young Investigator 3 Current address: Palomar Observatory, Caltech 105-24, Pasadena, CA 91125 4 At the time of writing Paper I, we were aware of only the zabs = 3:390 damped system; another (lower column density) LLS/damped system is present at zabs = 3:050 (Savaglio, D'Odorico, & Moller 1994). Only one candidate z > 3 galaxy was found near the QSO sightline.

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We measure the field galaxy luminosity function (LF) as a function of color and redshift from z = 0 to z = 0.5 using galaxies from the Norris Survey of the Corona Borealis Supercluster. The data set consists of 603 field galaxies with 0 < z ≤ 0.5 and spans a wide range in apparent magnitude (14.0 m ∼ < r ∼ < 21.5 m ), although our field galaxy LF analysis is limited to 493 galaxies with r ≤ 20.0 m . We use the observed g − r colors of the galaxies to compute accurate corrections to the rest B AB and r bands. We find that our local r-band LF, when normalized to counts in high galactic latitude fields, agrees well with the local LF measured in the Las Campanas Redshift Survey. Our B AB -band local LF, however, does not match the b j -band LF from the Stromlo/APM survey, having a normalization 1.6 times higher. We see compelling evidence that the B AB -band field galaxy LF evolves with redshift. The evolution is strongest for the population of star-forming galaxies with [O II] λ3727 rest-frame equivalent widths greater than 10Å. The population of red, quiescent galaxies shows no sign of evolution to z = 0.5. The evolution of the LF which we observe is consistent with the findings of other faint galaxy redshift surveys. The fraction of galaxies with [O II] emission increases rapidly with redshift, but the fraction of galaxies with strong Hδ absorption, a signature of a burst of star-formation, does not. We thus conclude that the star formation in distant galaxies is primarily long-lived.We also compute the LFs of the Corona Borealis supercluster (z ≈ 0.07, 419 galaxies with 14.1 m ≤ r ≤ 20.0 m ) and the Abell 2069 supercluster (z ≈ 0.11, 1 present address: Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK -2 -318 galaxies with 15.1 m ≤ r ≤ 20.0 m ). The shapes of the two supercluster luminosity functions are broadly similar to the shape of the local luminosity function. However, there are important differences. Both supercluster LFs have an excess of very bright galaxies. In addition, the characteristic magnitude of the Corona Borealis supercluster LF is roughly half a magnitude brighter than that of the local field galaxy LF, and there is a suggestion of an upturn in the LF for galaxies fainter than M(B AB ) ∼ −17 m .