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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/2504.20564 |
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| _version_ | 1866909596831973376 |
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| author | Fukayama, Takuro |
| author_facet | Fukayama, Takuro |
| contents | Let $X$ be a smooth projective curve over a finite field $\mathbb{F}_q$, $k$ be its function field, and $G$ be a simply connected almost simple split group over $\mathbb{F}_q$. We also write $G$ for its structure over $k$. We calculate the sum of multiplicities of all cuspidal representations of $G$ satisfying a given condition assuming the conjectural trace formula. We also observe how the sum changes if we replace $X$ by its base change $X\otimes_{\mathbb{F}_q}\mathbb{F}_{q^m}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_20564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The number of cuspidal representations over a function field and its behavior under base changes Fukayama, Takuro Number Theory Let $X$ be a smooth projective curve over a finite field $\mathbb{F}_q$, $k$ be its function field, and $G$ be a simply connected almost simple split group over $\mathbb{F}_q$. We also write $G$ for its structure over $k$. We calculate the sum of multiplicities of all cuspidal representations of $G$ satisfying a given condition assuming the conjectural trace formula. We also observe how the sum changes if we replace $X$ by its base change $X\otimes_{\mathbb{F}_q}\mathbb{F}_{q^m}$. |
| title | The number of cuspidal representations over a function field and its behavior under base changes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2504.20564 |