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Cosmological evolution of the QSO luminosity functions (LFs) atNIR/optical/X-ray bands for 1.3 < z < 3.5 is investigated based on therealistic QSO spectra. The accretion-disk theory predicts that although QSOluminosities only depend on mass-accretion rate, \Mdot, QSO spectra have adependence on black-hole mass, M_{BH}, as well. The smaller M_{BH} is and/orthe larger \Mdot is, the harder becomes the QSO NIR/optical/UV spectrum. Wemodel disk spectra which can reproduce these features and calculated LFs forredshift z ~ 3 with the assumption of new-born QSOs being shining at theEddington luminosity. The main results are: (i) the observed LFs at optical andX-rays can be simultaneously reproduced. (ii) LFs at optical and X-ray bandsare not sensitive to M_{BH}, while LFs at NIR bands are; about one order ofmagnitude difference is expected in volume number densities at L_{I, J} ~10^{46} erg s^{-1} between the case that all QSOs would have the same spectralshape as that of M_{BH} = 10^{9} M_sun and the case with M_{BH} = 10^{11}M_sun. (iii) The resultant LFs at NIR are dominated by 10^{7} M_sun black-holesat L_{I, J} ~ 10^{44} erg s^{-1}, and by 10^{11} M_sun black-holes at L_{I, J}\~ 10^{46} erg s^{-1}. Future infrared observations from space(e.g.NGST) willprobe cosmological evolution of black hole masses. For redshift z < 3, on theother hand, the observed optical/X-ray LFs can be fitted, if the initial QSOluminosity L_0 is below the Eddington luminosity. Interestingly, the bestfitting values of l = L_0/L_{Edd} are different in B- and X-ray bands; l_B ~2.5 l_X. The reason for this discrepancy is briefly discussed.Comment: 10 pages,7 Figures,to be published in Publications of the  Astronomical Society of Japa

Theoretical Models of Multi-Waveband QSO Luminosity Functions