The local exterior square L-function: Holomorphy, non-vanishing and Shalika functionals
DSpace at IIT Bombay
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Title |
The local exterior square L-function: Holomorphy, non-vanishing and Shalika functionals
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Creator |
KEWAT, PK
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Subject |
ADIC GROUPS
REPRESENTATIONS CONJECTURE GL(N) Representation theory Integral representations of L-functions |
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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.
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Publisher |
ACADEMIC PRESS INC ELSEVIER SCIENCE
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Date |
2012-06-26T07:09:01Z
2012-06-26T07:09:01Z 2011 |
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Type |
Article
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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 |
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Language |
English
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