Algebraic functions with infinitely many values in a number field

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 .

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Publication Details

Journal
Journal de Théorie des Nombres de Bordeaux
Published
2026-09-16
DOI
https://doi.org/10.5802/jtnb.1370
Primary Topic
Meromorphic and Entire Functions
Type
article
Field-Weighted Citation Impact
0.00

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article

Algebraic functions with infinitely many values in a number field

Fedor Pakovich
Journal de Théorie des Nombres de Bordeaux
Meromorphic and Entire Functions
article

Algebraic functions with infinitely many values in a number field

Fedor Pakovich
article en

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 .

Journal de Théorie des Nombres de BordeauxVol. 38(2)
Ben-Gurion University of the Negev (IL)
Israel Science Foundation
Openalex Percentile: Top 98%
Meromorphic and Entire Functions
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Algebraic functions with infinitely many values in a number field — Fedor Pakovich · Journal de Théorie des Nombres de Bordeaux (2026) | TGRS Research Map | TGRS