Geodesic
On Local L-Functions and Normalized Intertwining Operators
Canadian journal of mathematics, Tome 57 (2005) no. 3, pp. 535-597

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we make explicit all $L$ -functions in the Langlands–Shahidi method which appear as normalizing factors of global intertwining operators in the constant term of the Eisenstein series. We prove, in many cases, the conjecture of Shahidi regarding the holomorphy of the local $L$ -functions. We also prove that the normalized local intertwining operators are holomorphic and non-vaninishing for $\operatorname{Re}\left( s \right)\,\ge \,1/2$ in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrum and determining poles of automorphic $L$ -functions.
DOI : 10.4153/CJM-2005-023-x
Mots-clés : 11F70, 22E55 
Kim, Henry H. On Local L-Functions and Normalized Intertwining Operators. Canadian journal of mathematics, Tome 57 (2005) no. 3, pp. 535-597. doi: 10.4153/CJM-2005-023-x
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