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arXiv · 1701.04609

Finite beta-expansions with negative bases

Zuzana Krčmáriková·Wolfgang Steiner·Tomáš Vávra
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Abstract

The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $β$ having the negative finiteness property, that is the set of finite $(-β)$-expansions is equal to $\mathbb{Z}[β^{-1}]$. For a class of numbers including the Tribonacci number, we compute the maximal length of the fractional parts arising in the addition and subtraction of $(-β)$-integers. We also give conditions excluding the negative finiteness property.

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Zuzana Krčmáriková, Wolfgang Steiner, Tomáš Vávra. 2017-01-17. Finite beta-expansions with negative bases. https://arxiv.org/abs/1701.04609

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