ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER Fq((x−1))
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In [6], it is proved that the lengths of periods occurring in the β-expansion of a rational series r noted by Perβ(r) depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic β-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if r = P/Q is written in reduced form with |P| < |Q|, we will generalize the curious property “Perβ(P/Q) = Perβ(1/Q)”.
Abstract
In [6], it is proved that the lengths of periods occurring in the β-expansion of a rational series r noted by Perβ(r) depend only on the denominator of the reduced form of r for quadratic Pisot unit series. In this paper, we will show first that every rational r in the unit disk has strictly periodic β-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if r = P/Q is written in reduced form with |P| < |Q|, we will generalize the curious property “Perβ(P/Q) = Perβ(1/Q)”.
참고문헌 (13)
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