Mass equidistribution for Saito-Kurokawa lifts

Abstract

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 $k⟶\infty$. As a corollary, we show under GRH that the zero divisors of Saito--Kurokawa lifts equidistribute as their weights tend to infinity.

Accepted version, to appear in GAFA; 58 pages