Waring Numbers of Ramified $p$-adic Rings
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arXiv
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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912466893537280 |
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| author | Anthony, Lucas Burton, Joe Deegbe, Irene England, Sarah Hamblen, Spencer Knowles, Reagan Stewart, Luke Wright, Hannah |
| author_facet | Anthony, Lucas Burton, Joe Deegbe, Irene England, Sarah Hamblen, Spencer Knowles, Reagan Stewart, Luke Wright, Hannah |
| contents | Let $p$ be prime and $e,k$ be positive integers, and let $R = {\mathbb Z}_p[\sqrt[e]{p}]$. We calculate the Waring numbers $g_R(k)$ for many values of $p, e$, and $k$, and investigate how the Waring numbers for $p=2$ change as $e$ and $k$ vary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_14624 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Waring Numbers of Ramified $p$-adic Rings Anthony, Lucas Burton, Joe Deegbe, Irene England, Sarah Hamblen, Spencer Knowles, Reagan Stewart, Luke Wright, Hannah Number Theory 11P05 (primary), 11E95, 11E25, 12D15 Let $p$ be prime and $e,k$ be positive integers, and let $R = {\mathbb Z}_p[\sqrt[e]{p}]$. We calculate the Waring numbers $g_R(k)$ for many values of $p, e$, and $k$, and investigate how the Waring numbers for $p=2$ change as $e$ and $k$ vary. |
| title | Waring Numbers of Ramified $p$-adic Rings |
| topic | Number Theory 11P05 (primary), 11E95, 11E25, 12D15 |
| url | https://arxiv.org/abs/2407.14624 |