Recent surveys have detected Ly \alpha emission from z = 4.5 - 6.5 at luminosities as low as 10 ^ { 41 } erg s ^ { -1 } .
There is good evidence that low numbers of AGN are among observed faint Ly \alpha emitters .
Combining these observations with an empirical relation between the intrinsic Ly \alpha and B-band luminosities of AGN , we obtain an upper limit on the number density of AGN with absolute magnitudes M _ { B } \in [ -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 _ { l } < 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 _ { l } < 0 , at magnitudes fainter than M _ { B } \sim - 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 } ~ { } \hbox to 0.0 pt { $ > $ } { \lower 4.3 pt \hbox { $ \sim$ } } -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 } M _ { \odot } .
To facilitate the identification of AGN among observed Ly \alpha emitters , we derive observational properties of faint AGN in the Ly \alpha line , as well as in the X-ray and optical bands .