Test vectors for Rankin–Selberg L-functions

Andrew R Booker, M Krishnamurthy, Min Lee

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We study the local zeta integrals attached to a pair of generic representations (π,τ) of GLn×GLm, n>m, over a p-adic field. Through a process of unipotent averaging we produce a pair of corresponding Whittaker functions whose zeta integral is non-zero, and we express this integral in terms of the Langlands parameters of π and τ. In many cases, these Whittaker functions also serve as a test vector for the associated Rankin–Selberg (local) L-function.

Original languageEnglish
Pages (from-to)37-48
Number of pages12
JournalJournal of Number Theory
Volume209
Early online date4 Oct 2019
DOIs
Publication statusPublished - 1 Apr 2020

Keywords

  • Automorphic representations
  • Test vectors

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