Finite beta-expansions with negative bases

Abstract : 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.
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Acta Mathematica Hungarica, Springer Verlag, 2017, 152 (2), pp.485 - 504. 〈10.1007/s10474-017-0711-9〉
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https://hal.archives-ouvertes.fr/hal-01620765
Contributeur : Wolfgang Steiner <>
Soumis le : vendredi 20 octobre 2017 - 23:19:07
Dernière modification le : jeudi 11 janvier 2018 - 06:27:39

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

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