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On Local $L$-Functions and Normalized Intertwining Operators |
Canad. J. Math. 57(2005), 535-597
Published:2005-06-01
Printed: Jun 2005
Printed: Jun 2005
- Henry H. Kim
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 - 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] |