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| Format: | Preprint |
| Veröffentlicht: |
2023
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2307.16828 |
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| _version_ | 1866912125152133120 |
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| author | Goren, Eyal Z. Love, Jonathan R. |
| author_facet | Goren, Eyal Z. Love, Jonathan R. |
| contents | Let $\mathcal{O}$ be a maximal order in the quaternion algebra over $\mathbb{Q}$ ramified at $p$ and $\infty$. We prove two theorems that allow us to recover the structure of $\mathcal{O}$ from limited information. The first says that for any infinite set $S$ of integers coprime to $p$, $\mathcal{O}$ is spanned as a $\mathbb{Z}$-module by elements with norm in $S$. The second says that $\mathcal{O}$ is determined up to isomorphism by its theta function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16828 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On elements of prescribed norm in maximal orders of a quaternion algebra Goren, Eyal Z. Love, Jonathan R. Number Theory 11R52, 11H55 Let $\mathcal{O}$ be a maximal order in the quaternion algebra over $\mathbb{Q}$ ramified at $p$ and $\infty$. We prove two theorems that allow us to recover the structure of $\mathcal{O}$ from limited information. The first says that for any infinite set $S$ of integers coprime to $p$, $\mathcal{O}$ is spanned as a $\mathbb{Z}$-module by elements with norm in $S$. The second says that $\mathcal{O}$ is determined up to isomorphism by its theta function. |
| title | On elements of prescribed norm in maximal orders of a quaternion algebra |
| topic | Number Theory 11R52, 11H55 |
| url | https://arxiv.org/abs/2307.16828 |