Let F be a holomorphic cuspidal Hecke eigenform for \(\mathrm{Sp}_{4}({\mathbb{Z}})\) of weight k that is a Saito–Kurokawa lift. Assuming the Generalized Riemann Hypothesis (GRH), we prove that the mass of F equidistributes on the Siegel modular variety as k⟶∞. As a corollary, we show under GRH that the zero divisors of Saito–Kurokawa lifts equidistribute as their weights tend to infinity.

中文翻译：

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Saito-Kurokawa 电梯的质量均匀分配

令 F 为权重 k 的 \(\mathrm{Sp}_{4}({\mathbb{Z}})\) 的全纯尖头赫克本征型，即 Saito-Kurokawa 升力。假设广义黎曼假设（GRH），我们证明 F 的质量在西格尔模簇上均匀分布为 k⟶∞。作为推论，我们在 GRH 下证明，Saito-Kurokawa 升力的零因子是均匀分布的，因为它们的权重趋于无穷大。