Mass Equidistribution for Saito-Kurokawa Lifts
: Jääsaari, Jesse; Lester, Stephen; Saha, Abhishek
Publisher: Springer Nature
: 2024
: Geometric And Functional Analysis
: Geometric and Functional Analysis
: 34
: 5
: 1460
: 1532
: 1016-443X
: 1420-8970
DOI: https://doi.org/10.1007/s00039-024-00690-x(external)
: https://link.springer.com/article/10.1007/s00039-024-00690-x(external)
: https://research.utu.fi/converis/portal/detail/Publication/457359572(external)
Let F be a holomorphic cuspidal Hecke eigenform for 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.
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This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/T028343/1].