Zeros of Rankin–Selberg L-functions in families

Let Fₙ be the set of all cuspidal automorphic representations π of GLₙ with unitary central character over a number field F . We prove the first unconditional zero density estimate for the set S=(s,π × π ') π ∈ Fₙ\ of Rankin–Selberg L -functions, where π '∈ Fn' is fixed. We use this density estimate to establish: (i) a hybrid-aspect subconvexity bound at s=1/2 for almost all L(s,π × π ')∈ S ; (ii) a strong on-average form of effective multiplicity one for almost all π ∈ Fₙ ; and (iii) a positive level of distribution for L(s,π × π ) , in the sense of Bombieri–Vinogradov, for each π ∈ Fₙ .