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On Local L-Functions and Normalized Intertwining Operators
- Source :
- Canadian Journal of Mathematics. 57:535-597
- Publication Year :
- 2005
- Publisher :
- Canadian Mathematical Society, 2005.
-
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) ≥ 1/2 in many cases. These local results are essential in global applications such as Langlands functoriality, residual spectrumand determining poles of automorphic L-functions.
- Subjects :
- Pure mathematics
Conjecture
General Mathematics
010102 general mathematics
Spectrum (functional analysis)
Holomorphic function
Residual
Constant term
01 natural sciences
Algebra
symbols.namesake
0103 physical sciences
Eisenstein series
symbols
010307 mathematical physics
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 14964279 and 0008414X
- Volume :
- 57
- Database :
- OpenAIRE
- Journal :
- Canadian Journal of Mathematics
- Accession number :
- edsair.doi...........4531bb86eccde98b155596dcfe2fd897