Algebraic functions with infinitely many values in a number field

2024/12/17 by Pakovich, Fedor · 1 citation
#Algebraic Geometry (math.AG) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2412.13384

Abstract

We describe 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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