A multi-variable Rankin–Selberg integral for a product of GL2 -twisted Spinor L-functions

Joseph Hundley; Xin Shen

doi:10.1007/s00605-015-0868-7

A multi-variable Rankin–Selberg integral for a product of GL₂ -twisted Spinor L-functions

Joseph Hundley
, Xin Shen

Mathematics

University of Toronto

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

2 Scopus citations

Abstract

We consider a new integral representation for L(s₁, Π × τ₁) L(s₂, Π × τ₂) , where Π is a globally generic cuspidal representation of GSp₄, and τ₁ and τ₂ are two cuspidal representations of GL₂ having the same central character. As and application, we find a new period condition for two such L functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on GSO(12) and a theta function on Sp(16). A similar integral on GSO(18) fails to unfold completely, but in a way that provides further evidence of a connection.

Original language	English
Pages (from-to)	355-403
Number of pages	49
Journal	Monatshefte fur Mathematik
Volume	181
Issue number	2
DOIs	https://doi.org/10.1007/s00605-015-0868-7
State	Published - Oct 1 2016

Keywords

Fourier coefficient
Integral representation
Rankin–Selberg
Spinor L-function
Theta correspondence

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title = "A multi-variable Rankin–Selberg integral for a product of GL2 -twisted Spinor L-functions",

abstract = "We consider a new integral representation for L(s1, Π × τ1) L(s2, Π × τ2) , where Π is a globally generic cuspidal representation of GSp4, and τ1 and τ2 are two cuspidal representations of GL2 having the same central character. As and application, we find a new period condition for two such L functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on GSO(12) and a theta function on Sp(16). A similar integral on GSO(18) fails to unfold completely, but in a way that provides further evidence of a connection.",

keywords = "Fourier coefficient, Integral representation, Rankin–Selberg, Spinor L-function, Theta correspondence",

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T1 - A multi-variable Rankin–Selberg integral for a product of GL2 -twisted Spinor L-functions

AU - Hundley, Joseph

AU - Shen, Xin

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We consider a new integral representation for L(s1, Π × τ1) L(s2, Π × τ2) , where Π is a globally generic cuspidal representation of GSp4, and τ1 and τ2 are two cuspidal representations of GL2 having the same central character. As and application, we find a new period condition for two such L functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on GSO(12) and a theta function on Sp(16). A similar integral on GSO(18) fails to unfold completely, but in a way that provides further evidence of a connection.

AB - We consider a new integral representation for L(s1, Π × τ1) L(s2, Π × τ2) , where Π is a globally generic cuspidal representation of GSp4, and τ1 and τ2 are two cuspidal representations of GL2 having the same central character. As and application, we find a new period condition for two such L functions to have a pole simultaneously. This points to an intriguing connection between a Fourier coefficient of a residual representation on GSO(12) and a theta function on Sp(16). A similar integral on GSO(18) fails to unfold completely, but in a way that provides further evidence of a connection.

KW - Fourier coefficient

KW - Integral representation

KW - Rankin–Selberg

KW - Spinor L-function

KW - Theta correspondence

UR - https://www.scopus.com/pages/publications/84953312638

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DO - 10.1007/s00605-015-0868-7

M3 - Article

AN - SCOPUS:84953312638

SN - 0026-9255

VL - 181

SP - 355

EP - 403

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

IS - 2

ER -

A multi-variable Rankin–Selberg integral for a product of GL₂ -twisted Spinor L-functions

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