Mass equidistribution for Saito-Kurokawa lifts

TY - JOUR

T1 - Mass equidistribution for Saito-Kurokawa lifts

AU - Jaasaari, Jesse

AU - Lester, Stephen

AU - Saha, Abhishek

PY - 2024/7/2

Y1 - 2024/7/2

N2 - Let $F$ be a holomorphic cuspidal Hecke eigenform for $\Sp_4(\Z)$ 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 $k\longrightarrow \infty$. As a corollary, we show under GRH that the zero divisors of Saito--Kurokawa lifts equidistribute as their weights tend to infinity.

AB - Let $F$ be a holomorphic cuspidal Hecke eigenform for $\Sp_4(\Z)$ 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 $k\longrightarrow \infty$. As a corollary, we show under GRH that the zero divisors of Saito--Kurokawa lifts equidistribute as their weights tend to infinity.

M3 - Article

SN - 1016-443X

JO - GEOMETRIC AND FUNCTIONAL ANALYSIS

JF - GEOMETRIC AND FUNCTIONAL ANALYSIS

ER -