Binary quadratic forms with the same value set
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913334173892608 |
|---|---|
| author | Fouvry, Étienne Koymans, Peter |
| author_facet | Fouvry, Étienne Koymans, Peter |
| contents | Given a binary quadratic form $F \in \mathbb{Z}[X, Y]$, we define its value set $F(\mathbb{Z}^2)$ to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. If $F$ and $G$ are two binary quadratic forms with integer coefficients, we give necessary and sufficient conditions on $F$ and $G$ for $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09575 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Binary quadratic forms with the same value set Fouvry, Étienne Koymans, Peter Number Theory Given a binary quadratic form $F \in \mathbb{Z}[X, Y]$, we define its value set $F(\mathbb{Z}^2)$ to be $\{F(x, y) : (x, y) \in \mathbb{Z}^2\}$. If $F$ and $G$ are two binary quadratic forms with integer coefficients, we give necessary and sufficient conditions on $F$ and $G$ for $F(\mathbb{Z}^2) = G(\mathbb{Z}^2)$. |
| title | Binary quadratic forms with the same value set |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.09575 |