New optimal function field towers over finite fields of quartic power
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909879747215360 |
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| author | Hu, Chuangqiang Zhu, Xiuwu |
| author_facet | Hu, Chuangqiang Zhu, Xiuwu |
| contents | We introduce two new types of towers of Drinfeld modular curves. These towers originate from a specific domain $\mathcal{A} $ and are analogous to the towers of rank-two Drinfeld modular curves over the polynomial ring. Specifically, the domain $\mathcal{A} $ corresponds to the projective line over the finite field $ \mathbb{F}_q $, equipped with an infinite place of degree two. We select an arbitrary non-zero principal $\mathcal{A} $-ideal $ I_η $ of degree two. Notably, the $ I_η $-reduction of the tower of minimal Drinfeld modular curves is asymptotically optimal over the finite field $ \mathbb{F}_{q^4} $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27159 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New optimal function field towers over finite fields of quartic power Hu, Chuangqiang Zhu, Xiuwu Number Theory We introduce two new types of towers of Drinfeld modular curves. These towers originate from a specific domain $\mathcal{A} $ and are analogous to the towers of rank-two Drinfeld modular curves over the polynomial ring. Specifically, the domain $\mathcal{A} $ corresponds to the projective line over the finite field $ \mathbb{F}_q $, equipped with an infinite place of degree two. We select an arbitrary non-zero principal $\mathcal{A} $-ideal $ I_η $ of degree two. Notably, the $ I_η $-reduction of the tower of minimal Drinfeld modular curves is asymptotically optimal over the finite field $ \mathbb{F}_{q^4} $. |
| title | New optimal function field towers over finite fields of quartic power |
| topic | Number Theory |
| url | https://arxiv.org/abs/2510.27159 |