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We match quasars discovered in a multi-color survey centered on the northernHubble Deep Field (HDF) with radio sources from an ultra-deep radio survey.Although 3 out of 12 quasars are detected at a level below 0.2 mJy at 1.4 GHz,all of the quasars in the search area are radio-quiet by the criterion L_r <10^{25} h^{-1}_{50} W/Hz. We combine this information with other radio surveysof quasars so as to break the degeneracy between redshift and luminosity. Inthe redshift range 0.02 < z < 3.64, the radio-loud fraction increases withincreasing optical luminosity, consistent with some degree of correlationbetween the non-thermal optical and radio emissions. More tentatively, for lowluminosity quasars in the range -22.5 < M_B < -25, the radio-loud fractiondecreases with increasing redshift. We can infer from this that the radioluminosity function evolves more slowly than the optical luminosity function.The mechanism that leads to strong radio emission in only a small fraction ofquasars at any epoch is still unknown.Comment: Accepted by the Astrophysical Journal; 16 pages total (includes 4  figures and 2 tables

Radio‐quiet Quasars in the Direction of the Northern Hubble Deep Field