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ON THE DEGREE OF CERTAIN LOCAL L-FUNCTIONS

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Title ON THE DEGREE OF CERTAIN LOCAL L-FUNCTIONS
 
Creator ANANDAVARDHANAN, UK
MONDAL, AK
 
Subject RANKIN-SELBERG CONVOLUTIONS
SQUARE L-FUNCTIONS
ASAI L-FUNCTIONS
DISTINGUISHED REPRESENTATIONS
PLANCHEREL MEASURES
UNITARY GROUPS
ADIC GROUPS
REDUCIBILITY
GL(N)
CONJECTURE
Asai L-function
symmetric square L-function
exterior square L-function
degree of a local L-function
 
Description Let pi be an irreducible supercuspidal representation of GL(n)(F), where F is a p-adic field. By a result of Bushnell and Kutzko, the group of unramified self-twists of pi has cardinality n/e, where e is the o(F)-period of the principal o(F)-order in M-n(F) attached to pi. This is the degree of the local Rankin-Selberg L-function L(s, pi x pi(boolean OR)). In this paper, we compute the degree of the Asai, symmetric square, and exterior square L-functions associated to pi. As an application, assuming p is odd, we compute the conductor of the Asai lift of a supercuspidal representation, where we also make use of the conductor formula for pairs of supercuspidal representations due to Bushnell, Henniart, and Kutzko (1998).
 
Publisher PACIFIC JOURNAL MATHEMATICS
 
Date 2016-01-15T10:32:46Z
2016-01-15T10:32:46Z
2015
 
Type Article
 
Identifier PACIFIC JOURNAL OF MATHEMATICS, 276(1)1-17
0030-8730
http://dx.doi.org/10.2140/pjm.2015.276.1
http://dspace.library.iitb.ac.in/jspui/handle/100/18355
 
Language en