A Siegel-Weil Identity for G2 and Poles of L-Functions

David Ginzburg, Dihua Jiang

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)256-287
Number of pages32
JournalJournal of Number Theory
Volume82
Issue number2
DOIs
StatePublished - Jun 2000

Bibliographical note

Funding Information:
1The second named author was partly supported by NSF Grant DMS-9896257.

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