On counting cuspidal automorphic representations for GSp(4)
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| Název: | On counting cuspidal automorphic representations for GSp(4) |
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| Autoři: | Roy, Manami, Schmidt, Ralf, Yi, Shaoyun |
| Zdroj: | Forum Mathematicum. 33:821-843 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Walter de Gruyter GmbH, 2021. |
| Rok vydání: | 2021 |
| Témata: | Arthur packets, Mathematics - Number Theory, cuspidal automorphic representations, dimension formulas, FOS: Mathematics, 11F46, 11F70, Plancherel measure, Number Theory (math.NT), 0101 mathematics, 01 natural sciences, Siegel cusp forms |
| Popis: | We find the number s k ( p , Ω ) s_{k}(p,\Omega) of cuspidal automorphic representations of GSp ( 4 , A Q ) \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 ≥ 3 k\geq 3 , and the non-archimedean component at 𝑝 is an Iwahori-spherical representation of type Ω and unramified otherwise. Using the automorphic Plancherel density theorem, we show how a limit version of our formula for s k ( p , Ω ) s_{k}(p,\Omega) generalizes to the vector-valued case and a finite number of ramified places. |
| Druh dokumentu: | Article Other literature type |
| Popis souboru: | Text |
| Jazyk: | English |
| ISSN: | 1435-5337 0933-7741 |
| DOI: | 10.1515/forum-2020-0313 |
| DOI: | 10.48550/arxiv.2010.09996 |
| Přístupová URL adresa: | http://arxiv.org/pdf/2010.09996 http://arxiv.org/abs/2010.09996 https://digital.library.unt.edu/ark:/67531/metadc1838861/m2/1/high_res_d/2010.09996.pdf https://www.degruyter.com/document/doi/10.1515/forum-2020-0313/html https://digital.library.unt.edu/ark:/67531/metadc1838861/ https://ui.adsabs.harvard.edu/abs/2020arXiv201009996R/abstract https://arxiv.org/abs/2010.09996 http://export.arxiv.org/pdf/2010.09996 https://arxiv.org/pdf/2010.09996.pdf |
| Rights: | arXiv Non-Exclusive Distribution |
| Přístupové číslo: | edsair.doi.dedup.....9d6cbdd3da2ac5d3d99f01182ea8a337 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | We find the number s k ( p , Ω ) s_{k}(p,\Omega) of cuspidal automorphic representations of GSp ( 4 , A Q ) \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 ≥ 3 k\geq 3 , and the non-archimedean component at 𝑝 is an Iwahori-spherical representation of type Ω and unramified otherwise. Using the automorphic Plancherel density theorem, we show how a limit version of our formula for s k ( p , Ω ) s_{k}(p,\Omega) generalizes to the vector-valued case and a finite number of ramified places. |
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| ISSN: | 14355337 09337741 |
| DOI: | 10.1515/forum-2020-0313 |