On counting cuspidal automorphic representations for $\mathrm{GSp}(4)$
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.09996
- arXiv:
- arXiv:2010.09996
- Bibcode:
- 2020arXiv201009996R
- Keywords:
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- Mathematics - Number Theory;
- 11F46;
- 11F70
- E-Print:
- Some minor changes are made. To appear in Forum Mathematicum