Lifting problem for universal quadratic forms over totally real cubic number fields
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909135268741120 |
|---|---|
| author | Kim, Daejun Lee, Seok Hyeong |
| author_facet | Kim, Daejun Lee, Seok Hyeong |
| contents | Lifting problem for universal quadratic forms asks for totally real number fields $K$ that admit a positive definite quadratic form with coefficients in $\mathbb{Z}$ that is universal over the ring of integers of $K$. In this paper, we show that $K=\mathbb{Q}(ζ_7+ζ_7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_07118 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lifting problem for universal quadratic forms over totally real cubic number fields Kim, Daejun Lee, Seok Hyeong Number Theory 11E12, 11R16, 11H06, 11H55 Lifting problem for universal quadratic forms asks for totally real number fields $K$ that admit a positive definite quadratic form with coefficients in $\mathbb{Z}$ that is universal over the ring of integers of $K$. In this paper, we show that $K=\mathbb{Q}(ζ_7+ζ_7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field. |
| title | Lifting problem for universal quadratic forms over totally real cubic number fields |
| topic | Number Theory 11E12, 11R16, 11H06, 11H55 |
| url | https://arxiv.org/abs/2307.07118 |