Mass Equidistribution for Saito-Kurokawa Lifts

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2024年7月23日

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Jesse Jääsaari,
Stephen Lester,
Abhishek Saha

摘要

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.