Periodic representations in algebraic bases
| Autor: | Tomáš Vávra, Vítězslav Kala |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Number Theory
010505 oceanography BETA (programming language) General Mathematics 11A63 11K16 010102 general mathematics 01 natural sciences Combinatorics Base (group theory) Unit circle Integer 0101 mathematics Element (category theory) Algebraic number Alphabet Representation (mathematics) computer 0105 earth and related environmental sciences Mathematics computer.programming_language |
| Zdroj: | Monatshefte für Mathematik. 188:109-119 |
| ISSN: | 1436-5081 0026-9255 |
| DOI: | 10.1007/s00605-017-1151-x |
| Popis: | We study periodic representations in number systems with an algebraic base $$\beta $$ (not a rational integer). We show that if $$\beta $$ has no Galois conjugate on the unit circle, then there exists a finite integer alphabet $$\mathcal A$$ such that every element of $$\mathbb Q(\beta )$$ admits an eventually periodic representation with base $$\beta $$ and digits in $$\mathcal A$$ . |
| Databáze: | OpenAIRE |
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