We present the J-band luminosity function of 1838 mid-infrared and X-ray selected AGNs in the redshift range 0<z<5.85. These luminosity functions are constructed by combining the deep multi-wavelength broad-band observations from the UV to the mid-IR of the NDWFS Bootes field with the X-ray observations of the XBootes survey and the spectroscopic observations of the same field by AGES. Our sample is primarily composed of IRAC-selected AGNs, targeted using modifications of the Stern et al.(2005) criteria, complemented by MIPS 24 microns and X-ray selected AGNs to alleviate the biases of IRAC mid-IR selection against z~4.5 quasars and AGNs faint with respect to their hosts. This sample provides an accurate link between low and high redshift AGN luminosity functions and does not suffer from the usual incompleteness of optical samples at z~3. We find that the space density of the brightest quasars strongly decreases from z=3 to z=0, while the space density of faint quasars is at least flat, and possibly increasing, over the same redshift range. At z>3 we observe a decrease in the space density of quasars of all brightnesses. We model the luminosity function by a double power-law and find that its evolution cannot be described by either pure luminosity or pure density evolution, but must be a combination of both. Our best-fit model has bright and faint power-law indices consistent with the low redshift measurements based on the 2QZ and 2SLAQ surveys and it generally agrees with the number of bright quasars predicted by other LFs at all redshifts. If we construct the QSO luminosity function using only the IRAC-selected AGNs, we find that the biases inherent to this selection method significantly modify the behavior of phi*(z) only for z<1 and have no significant impact upon the characteristic magnitude M*_J(z).
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