On the degree of certain local L-functions

U. K. Anandavardhanan, Amiya Kumar Mondal

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalPacific Journal of Mathematics
Issue number1
StatePublished - 2015
Externally publishedYes


  • Asai L-function
  • Degree of a local L-function
  • Exterior square L-function
  • Symmetric square L-function


Dive into the research topics of 'On the degree of certain local L-functions'. Together they form a unique fingerprint.

Cite this