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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.03068 |
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| _version_ | 1866916014619361280 |
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| author | Cheng, Yao |
| author_facet | Cheng, Yao |
| contents | The conjectural theory of local newofmrs for the split $p$-adic group ${\rm SO}_{2n+1}$, proposed by Gross, predicts that the space of local newforms in a generic representation is one-dimensional. In this note, we prove that this space is at most one-dimensional and verify its expected arithmetic properties, conditional on existence. These results play an important role in our proof of the existence part of the newform conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_03068 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness Cheng, Yao Number Theory The conjectural theory of local newofmrs for the split $p$-adic group ${\rm SO}_{2n+1}$, proposed by Gross, predicts that the space of local newforms in a generic representation is one-dimensional. In this note, we prove that this space is at most one-dimensional and verify its expected arithmetic properties, conditional on existence. These results play an important role in our proof of the existence part of the newform conjecture. |
| title | Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.03068 |