Algebraic functions with infinitely many values in a number field
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911105739128832 |
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| author | Pakovich, Fedor |
| author_facet | Pakovich, Fedor |
| contents | We describe algebraic curves $ X : F(x, y) = 0 $ defined over $\overline{\mathbb{Q}}$ that satisfy the following property: there exist a number field $k$ and an infinite set $S \subset k$ such that, for every $y \in S$, the roots of the polynomial $F(x, y)$ belong to $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13384 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic functions with infinitely many values in a number field Pakovich, Fedor Number Theory Algebraic Geometry Dynamical Systems We describe algebraic curves $ X : F(x, y) = 0 $ defined over $\overline{\mathbb{Q}}$ that satisfy the following property: there exist a number field $k$ and an infinite set $S \subset k$ such that, for every $y \in S$, the roots of the polynomial $F(x, y)$ belong to $k$. |
| title | Algebraic functions with infinitely many values in a number field |
| topic | Number Theory Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2412.13384 |