Purely periodic β-expansions in cubic Salem base in Fq((x−1))
Let Fq be the finite field with q elements and ? Salem series in Fq((X?1)). It is proved in [15] that, in this case, all elements in Fq(X,?) have purely periodic ?-expansion. We characterize the formal power series f in Fq(X,?) with purely periodic ?-expansions by the conjugate vector ~f when ? is a cubic unit. No similar results exist in the real case.
2017 ◽
Vol 2018
(15)
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pp. 4780-4798
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2003 ◽
Vol 75
(1)
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pp. 1-7
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Keyword(s):
2021 ◽
Vol 27
(1)
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pp. 115-122