Kuznetsov, Petersson and Weyl on GL(3), II: The generalized principal series forms

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