Abstract
Let \(\mathbb {F}_q\) be a finite field and \(\beta \) a Pisot or Salem unit series in \( \mathbb {F}_q((X^{-1}))\). The aim of this paper is to prove that the \(\beta \)-expansion of any rational element in the unit disk D(0, 1) is purely periodic. No similar result exist in the real case.
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Hariz, S.B., Hbaib, M. & Mahjoub, F. Purely periodic \(\beta \)-expansions with Pisot or Salem unit base in \(\mathbb {F}_q((X^{-1}))\) . Math. Z. 283, 679–684 (2016). https://doi.org/10.1007/s00209-016-1617-x
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DOI: https://doi.org/10.1007/s00209-016-1617-x