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The local exterior square L-function: Holomorphy, non-vanishing and Shalika functionals

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Title The local exterior square L-function: Holomorphy, non-vanishing and Shalika functionals
 
Creator KEWAT, PK
 
Subject ADIC GROUPS
REPRESENTATIONS
CONJECTURE
GL(N)
Representation theory
Integral representations of L-functions
 
Description Let pi be a smooth, irreducible, square integrable representation of GL(m)(F), where F is a non-archimedean local field of characteristic zero. We prove that the exterior square L-function L(JS)(s, pi, boolean AND(2)) defined via an integral representation due to Jacquet and Shalika is regular and non-vanishing in the region Re(s) > 0. We also investigate the behavior of the L-function L(JS)(S, pi, boolean AND(2)) at s = 0, and show that if the function L(JS)(s, pi, boolean AND(2)) has a pole at s = 0 then pi has a non-zero Shalika functional. (C) 2011 Elsevier Inc. All rights reserved.
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2012-06-26T07:09:01Z
2012-06-26T07:09:01Z
2011
 
Type Article
 
Identifier JOURNAL OF ALGEBRA,347(1)153-172
0021-8693
http://dx.doi.org/10.1016/j.jalgebra.2011.08.025
http://dspace.library.iitb.ac.in/jspui/handle/100/14097
 
Language English