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arXiv · 2010.09996

On counting cuspidal automorphic representations for $\mathrm{GSp}(4)$

Manami Roy·Ralf Schmidt·Shaoyun Yi
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Abstract

We find the number $s_k(p,\Omega)$ of cuspidal automorphic representations of $\mathrm{GSp}(4,\mathbb{A}_{\mathbb{Q}})$ with trivial central character such that the archimedean component is a holomorphic discrete series representation of weight $k\ge 3$, and the non-archimedean component at $p$ is an Iwahori-spherical representation of type $\Omega$ and unramified otherwise. Using the automorphic Plancherel density theorem, we show how a limit version of our formula for $s_k(p,\Omega)$ generalizes to the vector-valued case and a finite number of ramified places.

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Manami Roy, Ralf Schmidt, Shaoyun Yi. 2020-10-20. On counting cuspidal automorphic representations for $\mathrm{GSp}(4)$. https://doi.org/10.1515/forum-2020-0313

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