We prove an explicit central value formula for a family of complex L-series of degree 6 for GL2 × GL3 which arise as factors of certain Garret–Rankin triple product L-series associated with modular forms. Our result generalizes a previous formula of Ichino involving Saito–Kurokawa lifts, and as an application, we prove Deligne’s conjecture about the algebraicity of the central values of the considered L-series up to the relevant periods. I would also include some other arithmetic applications towards the subconvexity problem, construction of associated p-adic L function, etc.

This is joint work with Carlos de Vera Piquero.