On deligne's conjecture for certain automorphic l-functions for GL(3) × GL(2) and GL(4)

We prove Deligne's conjecture for certain automorphic L-functions for GL(3)×GL(2) and GL(4). The proof is based on rationality results for central critical values of triple product L-functions, which follow from establishing explicit Ichino's formulae for trilinear period integrals for Hilbert cusp forms on totally real étale cubic algebras over Q.