A proof of the refined Gan-Gross-Prasad conjecture for non-endoscopic Yoshida lifts

Andrew Corbett

doi:10.1515/forum-2015-0164

A proof of the refined Gan-Gross-Prasad conjecture for non-endoscopic Yoshida lifts

Andrew Corbett

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Abstract

We prove a precise formula relating the Bessel period of certain automorphic forms on GSp_4(F) to a central L-value. This is a special case of the refined Gan–Gross–Prasad conjecture for the groups (SO_5, SO_2) as set out by Ichino–Ikeda and Liu. This conjecture is deep and hard to prove in full generality; in this paper we succeed in proving the conjecture for forms lifted, via automorphic induction, from GL_2(E) where E is a quadratic extension of F. The case where E = FxF has been previously dealt with by Liu.

Original language	English
Pages (from-to)	59-90
Number of pages	37
Journal	Forum Mathematicum
Volume	29
Issue number	1
Early online date	5 May 2016
DOIs	https://doi.org/10.1515/forum-2015-0164
Publication status	Published - Jan 2017

Keywords

Automorphic periods
L-values
Gan-Gross-Prasad conjectures

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N2 - We prove a precise formula relating the Bessel period of certain automorphic forms on GSp_4(F) to a central L-value. This is a special case of the refined Gan–Gross–Prasad conjecture for the groups (SO_5, SO_2) as set out by Ichino–Ikeda and Liu. This conjecture is deep and hard to prove in full generality; in this paper we succeed in proving the conjecture for forms lifted, via automorphic induction, from GL_2(E) where E is a quadratic extension of F. The case where E = FxF has been previously dealt with by Liu.

AB - We prove a precise formula relating the Bessel period of certain automorphic forms on GSp_4(F) to a central L-value. This is a special case of the refined Gan–Gross–Prasad conjecture for the groups (SO_5, SO_2) as set out by Ichino–Ikeda and Liu. This conjecture is deep and hard to prove in full generality; in this paper we succeed in proving the conjecture for forms lifted, via automorphic induction, from GL_2(E) where E is a quadratic extension of F. The case where E = FxF has been previously dealt with by Liu.

KW - Automorphic periods

KW - L-values

KW - Gan-Gross-Prasad conjectures

UR - http://arxiv.org/abs/1507.00089

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DO - 10.1515/forum-2015-0164

M3 - Article (Academic Journal)

SN - 0933-7741

VL - 29

SP - 59

EP - 90

JO - Forum Mathematicum

JF - Forum Mathematicum

IS - 1

ER -

A proof of the refined Gan-Gross-Prasad conjecture for non-endoscopic Yoshida lifts

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