The GL(3) mellin transform for twisted non-cuspidal forms of higher level

The main result in this paper is the explicit computation of the functional equation satisfied by the GL(3) Mellin transform of a twisted non-cuspidal metaplectic form of non-trivial level. For concreteness, we work with one particular metaplectic form, automorphic under Gamma(3), although our metho ds extend without change to any form automorphic with respect to Gamma(p), p an odd prime. We clearly show the computations one must undertake in orde r to determine the pole locations of this transform (which depend on the fo rm in question), and carry out those straightforward computations in the ca se of our one specific form. This particular form, first considered by Bump and Hoffstein [BH], is the m aximal parabolic Eisenstein series on the cubic cover of GL(3) (induced Fro m the theta function on the cubic cover of GL(2)), which has the remarkable property that its Fourier coefficients are essentially Hecke cubic L-serie s. In joint work with Hoffstein, the authors have applied the main theorems in this paper to compute the average values of these Hecke cubic L-series, a result of great arithmetic interest.