Mass Equidistribution for Saito-Kurokawa Lifts

Abstract

AbstractLet 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.