A Siegel–Weil Identity for G2 and Poles of L-Functions Original Research Article

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 G2, we verify a portion of our conjecture for n=3, among some other results.