Test vectors for Rankin–Selberg L-functions

Andrew R Booker; M Krishnamurthy; Min Lee

doi:10.1016/j.jnt.2019.08.010

Test vectors for Rankin–Selberg L-functions

Andrew R Booker, M Krishnamurthy, Min Lee

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We study the local zeta integrals attached to a pair of generic representations (π,τ) of GL_n×GL_m, 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 language	English
Pages (from-to)	37-48
Number of pages	12
Journal	Journal of Number Theory
Volume	209
Early online date	4 Oct 2019
DOIs	https://doi.org/10.1016/j.jnt.2019.08.010
Publication status	Published - 1 Apr 2020

Keywords

Automorphic representations
Test vectors

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://www.sciencedirect.com/science/article/pii/S0022314X19302902#! . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 321 KBLicence: CC BY-NC-ND

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T1 - Test vectors for Rankin–Selberg L-functions

AU - Booker, Andrew R

AU - Krishnamurthy, M

AU - Lee, Min

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N2 - 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.

AB - 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.

KW - Automorphic representations

KW - Test vectors

UR - https://www.scopus.com/pages/publications/85074521487

U2 - 10.1016/j.jnt.2019.08.010

DO - 10.1016/j.jnt.2019.08.010

M3 - Article (Academic Journal)

AN - SCOPUS:85074521487

SN - 0022-314X

VL - 209

SP - 37

EP - 48

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

Test vectors for Rankin–Selberg L-functions

Abstract

Keywords

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