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

Abstract

We prove a precise formula relating the Bessel period of certain automorphic forms on ${\mathrm{GSp}}_4({\mathbb{A}}_F)$ to a central $L$-value. This is a special case of the refined Gan--Gross--Prasad conjecture for the groups $({\mathrm{SO}}_5,{\mathrm{SO}}_2)$ 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 ${\mathrm{GL}}_2({\mathbb{A}}_E)$ where $E$ is a quadratic extension of $F$. The case where $E=F\times F$ has been previously dealt with by Liu.

38 pages in Forum Mathematicum (2016)

References in corpus (1)

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups

Cited by in corpus (1)

• Explicit inner product formulas and Bessel period formulas for HST lifts