  The aim of the present article is to render the spectral theory of mean
values of automorphic $L$-functions -- in a unified fashion. This is an outcome
of the investigation commenced with the parts XII and XIV, where a framework
was laid on the basis of the theory of automorphic representations and a
general approach to the mean values was envisaged. We restrict ourselves to the
situation offered by the full modular group, solely for the sake of simplicity.
Details and extensions are to be published elsewhere. In this new version we
added details to all aspects of our argument especially for the treatment of
the discrete series and the continuous spectrum.
