Positive characteristic analogues of finite algebraic numbers
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918312907112448 |
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| author | Matsuzuki, Daichi Sakamoto, Honami Ueki, Jun |
| author_facet | Matsuzuki, Daichi Sakamoto, Honami Ueki, Jun |
| contents | J.~Rosen introduced the ring $\mathcal{P}^0_{\mathcal{A}}$ of so-called finite algebraic numbers, which may be seen as an analogue of certain periods in the ring $\mathcal{A}=\prod_p \mathbb{Z}/p\mathbb{Z} /\bigoplus_p \mathbb{Z}/p\mathbb{Z}$, $p$ running through all prime numbers. In this article, we introduce its positive characteristic analogue $\mathcal{P}^0_{\mathcal{A}_K}$ over the rational function field $K=\mathbb{F}_q(θ)$, $q$ being a prime power, and study foundational properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Positive characteristic analogues of finite algebraic numbers Matsuzuki, Daichi Sakamoto, Honami Ueki, Jun Number Theory Primary 11R58, 11B37, 11R45, Secondary 11A07, 11B39, 11J93 J.~Rosen introduced the ring $\mathcal{P}^0_{\mathcal{A}}$ of so-called finite algebraic numbers, which may be seen as an analogue of certain periods in the ring $\mathcal{A}=\prod_p \mathbb{Z}/p\mathbb{Z} /\bigoplus_p \mathbb{Z}/p\mathbb{Z}$, $p$ running through all prime numbers. In this article, we introduce its positive characteristic analogue $\mathcal{P}^0_{\mathcal{A}_K}$ over the rational function field $K=\mathbb{F}_q(θ)$, $q$ being a prime power, and study foundational properties. |
| title | Positive characteristic analogues of finite algebraic numbers |
| topic | Number Theory Primary 11R58, 11B37, 11R45, Secondary 11A07, 11B39, 11J93 |
| url | https://arxiv.org/abs/2601.21209 |