Pullbacks of Saito-Kurokawa lifts and a central value formula for degree 6 L-series

Abstract

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 stating the algebraicity of the central values of the considered L-series up to the relevant periods.