  This paper initiates the study by analytic methods of the generalized
principal series Maass forms on $GL(3)$. These forms occur as an infinite
sequence of one-parameter families in the two-parameter spectrum of $GL(3)$
Maass forms, analogous to the relationship between the holomorphic modular
forms and the spherical Maass cusp forms on $GL(2)$. We develop a Kuznetsov
trace formula attached to these forms at each weight and use it to prove an
arithmetically-weighted Weyl law, demonstrating the existence of forms which
are not self-dual. Previously, the only such forms that were known to exist
were the self-dual forms arising from symmetric-squares of $GL(2)$ forms. The
Kuznetsov formula developed here should take the place of the $GL(2)$ Petersson
trace formula for theorems "in the weight aspect". As before, the construction
involves evaluating the Archimedian local zeta integral for the Rankin-Selberg
convolution and proving a form of Kontorovich-Lebedev inversion.
