Spectral aspect subconvex bounds for Un+1× Un

Let (π, σ) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan–Gross–Prasad pair (Un+1, Un) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local conditions (in particular, temperedness). We prove that the subconvex bound L(π×σ,1/2)≪C(π×σ)1/4-δholds for any fixed δ