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 GSp4(AF) to a central L-value. This is a special case of the refined Gan–Gross–Prasad conjecture for the groups (SO5,SO2) as set out by Ichino–Ikeda [12] and Liu [14]. 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 GL2(AE) where E is a quadratic extension of F. The case where E=F×F has been previously dealt with by Liu [14].