A note on Sarnak's density hypothesis for $\textrm{Sp}_4$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909232636362752 |
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| author | Assing, Edgar |
| author_facet | Assing, Edgar |
| contents | In this note we prove Sarnak's (spherical) density hypothesis for the full discrete spectrum of the quotients $Γ_{\textrm{pa}}(q)\backslash \textrm{Sp}_4(\mathbb{R})$, where $Γ_{\textrm{pa}}(q)$ are paramodular groups with square-free level $q$. To derive this estimate we upgrade a density estimate established via the (pre)-Kuznetsov formula, which only accounts for the generic part, using Arthur's parametrization of the discrete spectrum. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_04791 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on Sarnak's density hypothesis for $\textrm{Sp}_4$ Assing, Edgar Number Theory 11F72, 11F46, 11F70 In this note we prove Sarnak's (spherical) density hypothesis for the full discrete spectrum of the quotients $Γ_{\textrm{pa}}(q)\backslash \textrm{Sp}_4(\mathbb{R})$, where $Γ_{\textrm{pa}}(q)$ are paramodular groups with square-free level $q$. To derive this estimate we upgrade a density estimate established via the (pre)-Kuznetsov formula, which only accounts for the generic part, using Arthur's parametrization of the discrete spectrum. |
| title | A note on Sarnak's density hypothesis for $\textrm{Sp}_4$ |
| topic | Number Theory 11F72, 11F46, 11F70 |
| url | https://arxiv.org/abs/2305.04791 |