TY - JOUR

T1 - On the degree of certain local L-functions

AU - Anandavardhanan, U. K.

AU - Mondal, Amiya Kumar

N1 - Publisher Copyright:
© 2015 Mathematical Sciences Publishers.

PY - 2015

Y1 - 2015

N2 - Let π be an irreducible supercuspidal representation of GLn(F), where F is a p-adic field. By a result of Bushnell and Kutzko, the group of unramified self-twists of π has cardinality n/e, where e is the oF-period of the principal oF-order in Mn(F) attached to π. This is the degree of the local Rankin-Selberg L-function L(s, π × π∨). In this paper, we compute the degree of the Asai, symmetric square, and exterior square L-functions associated to π. 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).

AB - Let π be an irreducible supercuspidal representation of GLn(F), where F is a p-adic field. By a result of Bushnell and Kutzko, the group of unramified self-twists of π has cardinality n/e, where e is the oF-period of the principal oF-order in Mn(F) attached to π. This is the degree of the local Rankin-Selberg L-function L(s, π × π∨). In this paper, we compute the degree of the Asai, symmetric square, and exterior square L-functions associated to π. 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).

KW - Asai L-function

KW - Degree of a local L-function

KW - Exterior square L-function

KW - Symmetric square L-function

UR - http://www.scopus.com/inward/record.url?scp=84938528956&partnerID=8YFLogxK

U2 - 10.2140/pjm.2015.276.1

DO - 10.2140/pjm.2015.276.1

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AN - SCOPUS:84938528956

SN - 0030-8730

VL - 276

SP - 1

EP - 17

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 1

ER -