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arXiv · 1709.04143

Periodic representations in algebraic bases

Vítězslav Kala·Tomáš Vávra
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Abstract

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

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Vítězslav Kala, Tomáš Vávra. 2017-09-13. Periodic representations in algebraic bases. https://doi.org/10.1007/s00605-017-1151-x

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