Northcott property and universality of higher degree forms
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929440558153728 |
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| author | Prakash, Om |
| author_facet | Prakash, Om |
| contents | Let $K$ be a totally real number field, $d$ a positive integer, and $Q$ a higher degree form over $K$. We prove that there are at most finitely many totally real extensions $L/K$ of degree $d$ such that $Q$ over $L$ is universal. Further, we show that there are no universal forms over totally real infinite extensions of $\mathbb{Q}$ having the Northcott property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19974 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Northcott property and universality of higher degree forms Prakash, Om Number Theory 11E10, 11E76, 11G50, 11H06, 11P05, 11R04, 11R20, 11R80 Let $K$ be a totally real number field, $d$ a positive integer, and $Q$ a higher degree form over $K$. We prove that there are at most finitely many totally real extensions $L/K$ of degree $d$ such that $Q$ over $L$ is universal. Further, we show that there are no universal forms over totally real infinite extensions of $\mathbb{Q}$ having the Northcott property. |
| title | Northcott property and universality of higher degree forms |
| topic | Number Theory 11E10, 11E76, 11G50, 11H06, 11P05, 11R04, 11R20, 11R80 |
| url | https://arxiv.org/abs/2407.19974 |