Class numbers of binary quadratic polynomials
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909468072083456 |
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| author | Yang, Zichen |
| author_facet | Yang, Zichen |
| contents | In this paper, we give a formula for the proper class number of a binary quadratic polynomial assuming that the conductor ideal is sufficiently divisible at dyadic places. This allows us to study the growth of the proper class numbers of totally positive binary quadratic polynomials. As an application, we prove finiteness results on totally positive binary quadratic polynomials with a fixed quadratic part and a fixed proper class number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Class numbers of binary quadratic polynomials Yang, Zichen Number Theory 11E08, 11E12, 11E16, 11E41 In this paper, we give a formula for the proper class number of a binary quadratic polynomial assuming that the conductor ideal is sufficiently divisible at dyadic places. This allows us to study the growth of the proper class numbers of totally positive binary quadratic polynomials. As an application, we prove finiteness results on totally positive binary quadratic polynomials with a fixed quadratic part and a fixed proper class number. |
| title | Class numbers of binary quadratic polynomials |
| topic | Number Theory 11E08, 11E12, 11E16, 11E41 |
| url | https://arxiv.org/abs/2409.06244 |