An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929300074135552 |
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| author | Porter, Christian |
| author_facet | Porter, Christian |
| contents | In this paper, we revisit the theory of perfect unary forms over real quadratic fields. Specifically, we deduce an infinite family of real quadratic fields $\mathbb{Q}(\sqrt{d})$ when $d=2$ or $3$ mod $4$, such that there are three classes of perfect unary forms up to homothety and equivalence. This work, along with the work in \cite{unitred}, seems to suggest that the number of classes of perfect unary forms is related to the fundamental unit of $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01538 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms Porter, Christian Number Theory In this paper, we revisit the theory of perfect unary forms over real quadratic fields. Specifically, we deduce an infinite family of real quadratic fields $\mathbb{Q}(\sqrt{d})$ when $d=2$ or $3$ mod $4$, such that there are three classes of perfect unary forms up to homothety and equivalence. This work, along with the work in \cite{unitred}, seems to suggest that the number of classes of perfect unary forms is related to the fundamental unit of $K$. |
| title | An Infinite Family of Real Quadratic Fields with Three Classes of Perfect Unary Forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.01538 |