ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER _q((x^-1)) = ON THE PERIOD OF β-EXPANSION OF PISOT OR SALEM SERIES OVER _q((x^-1))

다국어 초록 (Multilingual Abstract)

In [6], it is proved that the lengths of periods occurring in the ${\beta}$-expansion of a rational series r noted by $Per_{\beta}(r)$ 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 ${\beta}$-expansion for Pisot or Salem unit basis under some condition. Second, for this basis, if $r=\frac{P}{Q}$ is written in reduced form with |P| < |Q|, we will generalize the curious property "$Per_{\beta}(\frac{P}{Q})=Per_{\beta}(\frac{1}{Q})$".

참고문헌 (Reference)

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