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We report new Chandra observations of seven optically faint, z ~ 4 radio-quiet quasars (RQQs). We have combined these new observations with previous Chandra observations of RQQs to create a sample of 174 sources. These sources have 0.1 < z < 4.7, and 10 44 ergs s -1 < ν L ν (2500 Å) < 10 48 ergs s -1 . The X-ray detection fraction is 90%. We find that the X-ray loudness of RQQs decreases with UV luminosity and increases with redshift. The model that is best supported by the data has a linear dependence of optical to X-ray ratio α ox on cosmic time and a quadratic dependence of α ox on log L UV , where α ox becomes X-ray quiet more rapidly at higher log L UV . We find no significant evidence for a relationship between the X-ray photon index Γ x and the UV luminosity, and we find marginally significant evidence that the X-ray continuum flattens with increasing z (2 σ). The Γ x - z anticorrelation may be the result of X-ray spectral curvature, redshifting of a Compton reflection component into the observed Chandra band, and/or redshifting of a soft excess out of the observed Chandra band. Using the results for Γ x , we show that the α ox - z relationship is unlikely to be a spurious result caused by redshifting of the observable X-ray spectral region. A correlation between α ox and z implies evolution of the accretion process. We present a qualitative comparison of these new results with models for accretion disk emission.
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