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Article Dans Une Revue Acta Mathematica Hungarica Année : 2017

Finite beta-expansions with negative bases

Zuzana Krčmáriková
  • Fonction : Auteur
Tomáš Vávra
  • Fonction : Auteur

Résumé

The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $\beta$ having the negative finiteness property, that is the set of finite $(-\beta)$-expansions is equal to $\mathbb{Z}[\beta^{-1}]$. 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 $(-\beta)$-integers. We also give conditions excluding the negative finiteness property.

Dates et versions

hal-01620765 , version 1 (20-10-2017)

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Citer

Zuzana Krčmáriková, Wolfgang Steiner, Tomáš Vávra. Finite beta-expansions with negative bases. Acta Mathematica Hungarica, 2017, 152 (2), pp.485 - 504. ⟨10.1007/s10474-017-0711-9⟩. ⟨hal-01620765⟩
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