Local solubility of a family of ternary conics over a biprojective base I
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916398899396608 |
|---|---|
| author | Wilson, Cameron |
| author_facet | Wilson, Cameron |
| contents | Let $f,g\in\mathbb{Z}[u_1,u_2]$ be binary quadratic forms. We provide upper bounds for the number of rational points $(u,v)\in\mathbb{P}^1(\mathbb{Q})\times\mathbb{P}^1(\mathbb{Q})$ such that the ternary conic
\[
X_{(u,v)}: f(u_1,u_2)x^2 + g(v_1,v_2)y^2 = z^2
\] has a rational point. We also give some conditions under which lower bounds exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local solubility of a family of ternary conics over a biprojective base I Wilson, Cameron Number Theory 14G05, 11G99, 11N36 Let $f,g\in\mathbb{Z}[u_1,u_2]$ be binary quadratic forms. We provide upper bounds for the number of rational points $(u,v)\in\mathbb{P}^1(\mathbb{Q})\times\mathbb{P}^1(\mathbb{Q})$ such that the ternary conic \[ X_{(u,v)}: f(u_1,u_2)x^2 + g(v_1,v_2)y^2 = z^2 \] has a rational point. We also give some conditions under which lower bounds exist. |
| title | Local solubility of a family of ternary conics over a biprojective base I |
| topic | Number Theory 14G05, 11G99, 11N36 |
| url | https://arxiv.org/abs/2409.10688 |