A Family of New-Way Integrals for the Standard L-function of Cuspidal Representations of the Exceptional Group of Type G2

Avner Segal

doi:10.1093/imrn/rnw090

A Family of New-Way Integrals for the Standard L-function of Cuspidal Representations of the Exceptional Group of Type G₂

Avner Segal

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let L^S(s, π, Χ, st) be a standard twisted partial L-function of degree 7 of the cuspidal automorphic representation π of the exceptional group of type G₂. In this paper, we consider a family of Rankin-Selberg integrals and prove that it represents this L-function. As an application, we prove that the representations attaining certain prescribed poles are exactly the representations attained by θ-lift from a group of finite type.

Original language	English
Pages (from-to)	2014-2099
Number of pages	86
Journal	International Mathematics Research Notices
Volume	2017
Issue number	7
DOIs	https://doi.org/10.1093/imrn/rnw090
State	Published - 1 Apr 2017

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1093/imrn/rnw090

Cite this

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title = "A Family of New-Way Integrals for the Standard L-function of Cuspidal Representations of the Exceptional Group of Type G2",

abstract = "Let LS(s, π, Χ, st) be a standard twisted partial L-function of degree 7 of the cuspidal automorphic representation π of the exceptional group of type G2. In this paper, we consider a family of Rankin-Selberg integrals and prove that it represents this L-function. As an application, we prove that the representations attaining certain prescribed poles are exactly the representations attained by θ-lift from a group of finite type.",

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N2 - Let LS(s, π, Χ, st) be a standard twisted partial L-function of degree 7 of the cuspidal automorphic representation π of the exceptional group of type G2. In this paper, we consider a family of Rankin-Selberg integrals and prove that it represents this L-function. As an application, we prove that the representations attaining certain prescribed poles are exactly the representations attained by θ-lift from a group of finite type.

AB - Let LS(s, π, Χ, st) be a standard twisted partial L-function of degree 7 of the cuspidal automorphic representation π of the exceptional group of type G2. In this paper, we consider a family of Rankin-Selberg integrals and prove that it represents this L-function. As an application, we prove that the representations attaining certain prescribed poles are exactly the representations attained by θ-lift from a group of finite type.

UR - https://www.scopus.com/pages/publications/85020903345

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DO - 10.1093/imrn/rnw090

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JO - International Mathematics Research Notices

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