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The average dependence of the ratio of X-ray luminosity to optical luminosity as a function of redshift and optical luminosity for quasars is derived, and it is found that the explicit dependence of this ratio is predominantly on optical luminosity. For a wide class of models for the cosmological evolution of quasars, the results imply that the evolution of the X-ray luminosity function is weaker than the evolution of the optical luminosity function. Implications for physical models of quasars and for global properties of the quasar population are indicated.
Avni et al. (Mon,) studied this question.