Algebraic functions with infinitely many values in a number field
Abstract
We provide several characterizations of algebraic curves X : F ( x , y ) = 0 defined over ℚ ¯ that satisfy the following property: there exist a number field k and an infinite set S ⊂ k such that, for every y ∈ S , the roots of the polynomial F ( x , y ) belong to k .
Fields of Study & Subjects
Meromorphic and Entire Functions
Analytic Number Theory Research
advanced mathematical theories
Publication details
- Journal / source
- Journal de Théorie des Nombres de Bordeaux
- Volume
- 38
- Issue
- 2
- Pages
- 515–531
- Publication date
- 16 September 2026
- Language
- EN