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Quantum Unique Ergodicity for half-integral weight forms

We investigate the analogue of the Quantum Unique Ergodicity (QUE) conjecture for half-integral weight automorphic forms. Assuming the Generalized Riemann Hypothesis (GRH) we establish QUE for both half-integral weight holomorphic Hecke cusp forms for $Γ_0(4)$ lying in Kohnen's plus subspace and for half-integral weight Hecke Maaß cusp forms for $Γ_0(4)$ lying in Kohnen's plus subspace. By combining the former result along with an argument of Rudnick, it follows that under GRH the zeros of these holomorphic Hecke cusp equidistribute with respect to hyperbolic measure on $Γ_0(4)\backslash \mathbb H$ as the weight tends to infinity.