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.
- Automorphic periods
- Gan-Gross-Prasad conjectures