Functoriality for the classical groups over function fields

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Langlands' functoriality for generic representations from the split classical groups to an appropriate GLN is established. The functorial lift or transfer to GLN is obtained with the help of a converse theorem once the analytic properties of L-functions are studied using the Langlands-Shahidi approach. This paper is mostly devoted to understanding L-functions for the classical groups over a global function field, since the Langlands-Shahidi method has only been developed over number fields. To overcome many difficulties, stability of γ -factors under twists by highly ramified characters is used together with multiplicativity. Finally, by analyzing the image of functoriality, a proof of the Ramanujan conjecture for generic representations is obtained.

Original languageEnglish
Pages (from-to)4271-4335
Number of pages65
JournalInternational Mathematics Research Notices
Issue number22
StatePublished - 2009
Externally publishedYes


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