Periodic representations in algebraic bases

Abstrakt

We study periodic representations in number systems with an algebraic base (not a rational integer). We show that if has no Galois conjugate on the unit circle, then there exists a finite integer alphabet A such that every element of Q() admits an eventually periodic representation with base and digits in A.

Klíčová slova

• Pisot number
• Salem number
• Expansion in non-integer base
• Periodic representation