Universal quadratic forms and Dedekind zeta functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866912666713325568 |
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| author | Kala, Vítězslav Melistas, Mentzelos |
| author_facet | Kala, Vítězslav Melistas, Mentzelos |
| contents | We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the codifferent of $K$ is generated by a totally positive element. Motivated by a possible path to remove that assumption, we also investigate the smallest number of generators for the positive part of ideals in totally real numbers fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_12911 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universal quadratic forms and Dedekind zeta functions Kala, Vítězslav Melistas, Mentzelos Number Theory 11E12, 11E20, 11H06 We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the codifferent of $K$ is generated by a totally positive element. Motivated by a possible path to remove that assumption, we also investigate the smallest number of generators for the positive part of ideals in totally real numbers fields. |
| title | Universal quadratic forms and Dedekind zeta functions |
| topic | Number Theory 11E12, 11E20, 11H06 |
| url | https://arxiv.org/abs/2311.12911 |