CrossRef 2026

A note on Sarnak’s density hypothesis for $\operatorname{Sp}_{4}$

Edgar Assing

Abstrak

In this note, we prove Sarnak’s (spherical) density hypothesis for the full discrete spectrum of the quotients \Gamma_{\mathrm{pa}}(q) \backslash \operatorname{Sp}_{4}(\mathbb{R}) , where \Gamma_{\mathrm{pa}}(q) are paramodular groups with square-free level q . To derive this estimate we upgrade a density estimate established via the Kuznetsov formula, which only accounts for the generic part, using Arthur’s parametrization of the discrete spectrum.

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Edgar Assing

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Assing, E. (2026). A note on Sarnak’s density hypothesis for $\operatorname{Sp}_{4}$. https://doi.org/10.4171/cmh/612

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Tahun Terbit: 2026
Bahasa: en
Sumber Database: CrossRef
DOI: 10.4171/cmh/612
Akses: Terbatas