  We carried out extended spectroscopic confirmations of Ly-alpha emitters
(LAEs) at z=6.5 and 5.7 in the Subaru Deep Field. Now, the total number of
spectroscopically confirmed LAEs is 45 and 54 at z=6.5 and 5.7, respectively,
and at least 81% (70%) of our photometric candidates at z=6.5 (5.7) have been
spectroscopically identified as real LAEs. We made careful measurements of the
Ly-alpha luminosity, both photometrically and spectroscopically, to accurately
determine the Ly-alpha and rest-UV luminosity functions (LFs). The
substantially improved evaluation of the Ly-alpha LF at z=6.5 shows an apparent
deficit from z=5.7 at least at the bright end, and a possible decline even at
the faint end, though small uncertainties remain. The rest-UV LFs at z=6.5 and
5.7 are in good agreement, at least at the bright end, in clear contrast to the
differences seen in the Ly-alpha LF. These results imply an increase in the
neutral fraction of the intergalactic medium from z=5.7 to 6.5. The rest-frame
equivalent width (EW_0) distribution at z=6.5 seems to be systematically
smaller than z=5.7, and it shows an extended tail toward larger EW_0. The
bright end of the rest-UV LF can be reproduced from the observed Ly-alpha LF
and a reasonable EW_0-UV luminosity relation. Integrating this rest-UV LF
provides the first measurement of the contribution of LAEs to the photon budget
required for reionization. The derived UV LF suggests that the fractional
contribution of LAEs to the photon budget among Lyman break galaxies
significantly increases towards faint magnitudes. Low-luminosity LAEs could
dominate the ionizing photon budget, though this inference depends strongly on
the uncertain faint-end slope of the Ly-alpha LF.
