Zeros of Rankin–Selberg $L$-functions at the edge of the critical strip

Let $\pi$ and $\pi_0$ be unitary cuspidal automorphic representations. We prove log-free zero density estimates for Rankin-Selberg $L$-functions of the form $L(s,\pi\times\pi_0)$, where varies in a given family is fixed. These are unconditional many cases interest; they hold full generality assuming an average generalized Ramanujan conjecture. consider applications these related to mass equidistribution Hecke-Maass forms, rarity Landau-Siegel zeros $L$-functions, Chebotarev theorem, $\ell$-torsion class groups number fields.