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On Local $L$-Functions and Normalized Intertwining Operators

  Published:2005-06-01
 Printed: Jun 2005
  • Henry H. Kim
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Abstract

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 $\re(s)\geq 1/2$ in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrum and determining poles of automorphic $L$-functions.
MSC Classifications: 11F70, 22E55 show english descriptions Representation-theoretic methods; automorphic representations over local and global fields
Representations of Lie and linear algebraic groups over global fields and adele rings [See also 20G05]
11F70 - Representation-theoretic methods; automorphic representations over local and global fields
22E55 - Representations of Lie and linear algebraic groups over global fields and adele rings [See also 20G05]
 

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