Mass equidistribution for Saito-Kurokawa lifts
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916310024192000 |
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| author | Jääsaari, Jesse Lester, Stephen Saha, Abhishek |
| author_facet | Jääsaari, Jesse Lester, Stephen Saha, Abhishek |
| contents | 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 $k\longrightarrow \infty$. As a corollary, we show under GRH that the zero divisors of Saito--Kurokawa lifts equidistribute as their weights tend to infinity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2309_13009 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mass equidistribution for Saito-Kurokawa lifts Jääsaari, Jesse Lester, Stephen Saha, Abhishek Number Theory Analysis of PDEs Primary 11F46, Secondary 11F30, 11M41, 58J51 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 $k\longrightarrow \infty$. As a corollary, we show under GRH that the zero divisors of Saito--Kurokawa lifts equidistribute as their weights tend to infinity. |
| title | Mass equidistribution for Saito-Kurokawa lifts |
| topic | Number Theory Analysis of PDEs Primary 11F46, Secondary 11F30, 11M41, 58J51 |
| url | https://arxiv.org/abs/2309.13009 |