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On Local L-Functions and Normalized Intertwining Operators

Published online by Cambridge University Press:  20 November 2018

Henry H. Kim
Affiliation:
Deptartment of Mathematics, University of Toronto, Toronto, ON M5S 3G3, e-mail: henrykim@math.toronto.edu
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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 $\operatorname{Re}\left( s \right)\,\ge \,1/2$ in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrum and determining poles of automorphic $L$ -functions.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2005

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