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- W2950991992 abstract "We study the question of pure periodicity of expansions in the negative base numeration system. In analogy of Akiyama's result for positive Pisot unit base $beta$, we find a sufficient condition so that there exist an interval $J$ containing the origin such that the $(-beta)$-expansion of every rational number from $J$ is purely periodic. We focus on the case of quadratic bases and demonstrate the following difference between the negative and positive bases: It is known that the finiteness property (${rm Fin}(beta)=Z[beta]$) is not only sufficient, but also necessary in the case of positive quadratic and cubic bases. We show that ${rm Fin}(-beta)=Z[beta]$ is not necessary in the case of negative bases." @default.
- W2950991992 created "2019-06-27" @default.
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- W2950991992 date "2012-02-09" @default.
- W2950991992 modified "2023-09-27" @default.
- W2950991992 title "Purely periodic expansions in systems with negative base" @default.
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