Additively indecomposable quadratic forms over totally real number fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918156834963456 |
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| author | Tinková, Magdaléna Yatsyna, Pavlo |
| author_facet | Tinková, Magdaléna Yatsyna, Pavlo |
| contents | We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper bounds for the minimal ranks of $n$-universal quadratic forms. For $\mathbb{Q}(\sqrt{2}),~\mathbb{Q}(\sqrt{3}),~\mathbb{Q}(\sqrt{5}),~\mathbb{Q}(\sqrt{6})$, and $\mathbb{Q}(\sqrt{21})$, we classify, up to equivalence, all classical, additively indecomposable binary quadratic forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additively indecomposable quadratic forms over totally real number fields Tinková, Magdaléna Yatsyna, Pavlo Number Theory We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper bounds for the minimal ranks of $n$-universal quadratic forms. For $\mathbb{Q}(\sqrt{2}),~\mathbb{Q}(\sqrt{3}),~\mathbb{Q}(\sqrt{5}),~\mathbb{Q}(\sqrt{6})$, and $\mathbb{Q}(\sqrt{21})$, we classify, up to equivalence, all classical, additively indecomposable binary quadratic forms. |
| title | Additively indecomposable quadratic forms over totally real number fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.05991 |