A characterization of the distances between Pisot numbers generating the same number field
Abstract
Let $K$ be a real algebraic number field and let $\wp_{K}$ be the set of Pisot numbers generating $K$. We show that the elements of $\wp_{K}-\wp_{K}$ are the algebraic integers of $K$ whose images under the action of all embeddings of $K$ into $\mathbb{C}$, other than the identity of $K$, are of modulus less than $2$. This completes certain previous results due to Dubickas and the second author. Also, from the proof of this result, based on Minkowski's theorem on compact, convex and symmetric bodies, we deduce some related results.
Fields of Study & Subjects
Computability
Logic
AI Algorithms
semigroups and automata theory
Algorithms and Data Compression
Publication details
- Journal / source
- Publicationes Mathematicae Debrecen
- Volume
- 109
- Issue
- 1-2
- Pages
- 121–131
- Publication date
- 1 July 2026
- Language
- EN