Sábháilte in:
| Príomhchruthaitheoirí: | , , , |
|---|---|
| Formáid: | Preprint |
| Foilsithe / Cruthaithe: |
2024
|
| Ábhair: | |
| Rochtain ar líne: | https://arxiv.org/abs/2404.12844 |
| Clibeanna: |
Cuir clib leis
Níl clibeanna ann, Bí ar an gcéad duine le clib a chur leis an taifead seo!
|
| _version_ | 1866909580756254720 |
|---|---|
| author | Daans, Nicolas Kala, Vítězslav Krásenský, Jakub Yatsyna, Pavlo |
| author_facet | Daans, Nicolas Kala, Vítězslav Krásenský, Jakub Yatsyna, Pavlo |
| contents | We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_12844 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Failures of integral Springer's Theorem Daans, Nicolas Kala, Vítězslav Krásenský, Jakub Yatsyna, Pavlo Number Theory 11E12, 11H55, 11R80 We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed. |
| title | Failures of integral Springer's Theorem |
| topic | Number Theory 11E12, 11H55, 11R80 |
| url | https://arxiv.org/abs/2404.12844 |