Publications de l’Institut Mathématique, Nouvelle Série, Vol. 100[114], No. 1/1, pp. 279

Publications de l’Institut Mathématique, Nouvelle Série
Vol. 100[114], No. 1/1, pp. 279–285 (2016)

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PURELY PERIODIC $β$ -EXPANSIONS IN CUBIC SALEM BASE IN $𝔽_{q} ((X^{- 1}))$

Faïza Mahjoub

Department of Mathematics, Higher institute of applied science and technology, University of Monastir, Mahdia, Tunisia

Abstract: Let $𝔽_{q}$ be the finite field with $q$ elements and $β$ Salem series in $𝔽_{q} ((X^{- 1}))$ . It is proved in that, in this case, all elements in $𝔽_{q} (X, β)$ have purely periodic $β$ -expansion. We characterize the formal power series $f$ in $𝔽_{q} (X, β)$ with purely periodic $β$ -expansions by the conjugate vector $\tilde{f}$ when $β$ is a cubic unit. No similar results exist in the real case.

Keywords: formal power series; finite fields; $β$ -expansion; Salem element

Classification (MSC2000): 11R06; 37B50

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Electronic fulltext finalized on: 8 Nov 2016. This page was last modified: 14 Nov 2016.

© 2016 Mathematical Institute of the Serbian Academy of Science and Arts
© 2016 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition

PURELY PERIODIC β-EXPANSIONS IN CUBIC SALEM BASE IN 𝔽 q ((X -1 ))

Faïza Mahjoub

PURELY PERIODIC $β$ -EXPANSIONS IN CUBIC SALEM BASE IN $𝔽_{q} ((X^{- 1}))$