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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2511.08100 |
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| _version_ | 1866911259337687040 |
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| author | Koprowski, Przemysław |
| author_facet | Koprowski, Przemysław |
| contents | We study the class of polynomials that map a local field (i.e., the completion of a number field at a non-Archimedean place) into the subset of its $p$-th powers, where $p$ is the residue characteristic of the field in question. We present a characterization of such polynomials and show that this class is always much broader than the class of $p$-th powers of polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Polynomials assuming only local prime powers Koprowski, Przemysław Number Theory Primary: 11S05, 11C08, Secondary: 12J25 We study the class of polynomials that map a local field (i.e., the completion of a number field at a non-Archimedean place) into the subset of its $p$-th powers, where $p$ is the residue characteristic of the field in question. We present a characterization of such polynomials and show that this class is always much broader than the class of $p$-th powers of polynomials. |
| title | Polynomials assuming only local prime powers |
| topic | Number Theory Primary: 11S05, 11C08, Secondary: 12J25 |
| url | https://arxiv.org/abs/2511.08100 |