Purely periodic \(\beta\)-expansions in the quadratic base over the field of formal series (Q2907998)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Purely periodic \(\beta\)-expansions in the quadratic base over the field of formal series |
scientific article; zbMATH DE number 6076423
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Purely periodic \(\beta\)-expansions in the quadratic base over the field of formal series |
scientific article; zbMATH DE number 6076423 |
Statements
4 September 2012
0 references
formal power series
0 references
\(\beta \)-expansion
0 references
quadratic Pisot unit
0 references
0.9250045
0 references
0.9229602
0 references
0.9189468
0 references
0.91648966
0 references
0.9073653
0 references
0.90555865
0 references
0.8955755
0 references
Purely periodic \(\beta\)-expansions in the quadratic base over the field of formal series (English)
0 references
The authors define Pisot and Salem elements in the field of formal power series of the form \(f=\sum_{k=-\infty}^{l} f_k x^k\), where \(f_k\) belong to a finite field with \(q\) elements, as analogs of classical Pisot and Salem numbers. They study formal power series which have purely periodic \(\beta\)-expansions in the quadratic Pisot unit base \(\beta\). In particular, they show that every rational fraction \(f\) in the unit disc has a purely periodic \(\beta\)-expansion.
0 references
