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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2606.00633 |
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| _version_ | 1866916070531530752 |
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| author | Lai, Li Sprang, Johannes |
| author_facet | Lai, Li Sprang, Johannes |
| contents | The $P(t)$-adic Littlewood conjecture is a function field analogue of the famous $p$-adic Littlewood conjecture in Diophantine approximation. In this paper, we prove that the $P(t)$-adic Littlewood conjecture fails for any irreducible polynomial $P(t)$ over any ground field of odd characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00633 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $P(t)$-adic Littlewood conjecture in odd characteristics Lai, Li Sprang, Johannes Number Theory Algebraic Geometry 11J61 The $P(t)$-adic Littlewood conjecture is a function field analogue of the famous $p$-adic Littlewood conjecture in Diophantine approximation. In this paper, we prove that the $P(t)$-adic Littlewood conjecture fails for any irreducible polynomial $P(t)$ over any ground field of odd characteristic. |
| title | On the $P(t)$-adic Littlewood conjecture in odd characteristics |
| topic | Number Theory Algebraic Geometry 11J61 |
| url | https://arxiv.org/abs/2606.00633 |