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arXiv · 2305.04791

A note on Sarnak's density hypothesis for $\textrm{Sp}_4$

Edgar Assing
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Abstract

In this note we prove Sarnak's (spherical) density hypothesis for the full discrete spectrum of the quotients $\Gamma_{\textrm{pa}}(q)\backslash \textrm{Sp}_4(\mathbb{R})$, where $\Gamma_{\textrm{pa}}(q)$ 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.

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Edgar Assing. 2023-05-08. A note on Sarnak's density hypothesis for $\textrm{Sp}_4$. https://arxiv.org/abs/2305.04791

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