  Recent surveys have detected Lya emission from z=4.5-6.5 at luminosities as
low as 10^41 erg/s. There is good evidence that low numbers of AGN are among
observed faint Lya emitters. Combining these observations with an empirical
relation between the intrinsic Lya and B-band luminosities of AGN, we obtain an
upper limit on the number density of AGN with absolute magnitudes M_B=[-16,-19]
at z=4.5-6.5. These AGN are up to two orders of magnitude fainter than those
discovered in the Chandra Deep Field, resulting in the faintest observational
constraints to date at these redshifts. At z=4.5, the powerlaw slope of the
very faint end of the luminosity function of AGN is shallower than the slope
observed at lower redshifts, beta <1.6, at the 98% confidence level. In fact,
we find marginal evidence that the luminosity function rises with luminosity,
corresponding to a powerlaw slope beta <0, at magnitudes fainter than M_B~-20
(75% confidence level). These results suggest either that accretion onto lower
mass black holes is less efficient than onto their more massive counterparts,
or that the number of black holes powering AGN with M_B >-20 is lower than
expected from the M_BH-sigma relation by one-two orders of magnitude.
Extrapolating from reverberation-mapping studies suggests that these black
holes would have M_BH=10^6-10^7 Msun. To facilitate the identification of AGN
among observed Lya emitters, we derive observational properties of faint AGN in
the Lya line, as well as in the X-ray and optical bands.
