A Siegel-Well identity for G2 and poles of L-functions

Relations among endoscopy liftings of automorphic forms, poles of L-functions, and nonvanishing of certain periods of automorphic forms have long been expected, although they have not been formulated, even conjecturally. We take a first step toward considering the relations by formulating our conjectures for certain types of endoscopy liftings, which generalizes a theorem of Ginzburg et al. (1997, J. Reine Angew. Math. 487, 85-114) (n=2 case). By establishing the Siegel-Weil type identity for Eisenstein series of G(2), we verify a portion of our conjecture for n = 3, among some other results. (C) 2000 Academic Press.