On the height of polynomials that split completely over a fixed number field
Abstract
Let K / Q be a finite extension. We prove that the minimal height of polynomials of degree n of which all roots are in K × increases exponentially in n . We determine the implied constant exactly for totally real K and K equal to Q ( − 1 ) or Q ( − 3 ) .
Fields of Study & Subjects
Meromorphic and Entire Functions
Analytic Number Theory Research
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Indagationes Mathematicae
- Publication date
- 1 September 2026
- Language
- EN