TY - JOUR
T1 - A Siegel-Weil Identity for G2 and Poles of L-Functions
AU - Ginzburg, David
AU - Jiang, Dihua
N1 - Funding Information:
1The second named author was partly supported by NSF Grant DMS-9896257.
PY - 2000/6
Y1 - 2000/6
N2 - 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.
AB - 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.
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U2 - 10.1006/jnth.1999.2480
DO - 10.1006/jnth.1999.2480
M3 - Article
AN - SCOPUS:0345807510
SN - 0022-314X
VL - 82
SP - 256
EP - 287
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -