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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.16828 |
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Table of 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.