Gelbart, Stephen; Piatetski-Shapiro, Ilya I. Automorphic forms and L-functions for the unitary group. (English) Zbl 0531.10034 Lie group representations II, Proc. Spec. Year, Univ. Md., College Park 1982-83, Lect. Notes Math. 1041, 141-184 (1984). [For the entire collection see Zbl 0521.00012.] This is a summary with some proofs of the theory of automorphic forms, generalized Whittaker model, L-functions and \(\epsilon\)-factors for the unitary group \(U_{2,1}\) of three variables developed by the authors. The L-function for non-hypercuspidal representations is defined by the method of Rankin-Selberg-Jacquet and for hypercuspidal ones by the method of Shimura. The unitary group \((U_{1,1},U_{2,1})\) is regarded as a dual reductive pair in a 12-dimensional symplectic group and the lift of cusp forms from \(U_{1,1}\) to \(U_{2,1}\) is given by an integral against a theta-kernel; the image of this lift is characterized by the fact that the automorphic L-function \(L(s,\pi,\mu)\) has a pole for some \(\mu\). Reviewer: K.Lai Cited in 3 ReviewsCited in 17 Documents MSC: 11F27 Theta series; Weil representation; theta correspondences 11F70 Representation-theoretic methods; automorphic representations over local and global fields 22E55 Representations of Lie and linear algebraic groups over global fields and adèle rings Keywords:lifting of cusp forms; summary; automorphic forms; generalized Whittaker model; L-functions; \(\epsilon\)-factors; unitary group; dual reductive pair Citations:Zbl 0521.00012 PDFBibTeX XML