Beta-expansions of rational numbers in quadratic Pisot bases
نویسندگان
چکیده
We study rational numbers with purely periodic Rényi β-expansions. For bases β satisfying β2 = aβ + b with b dividing a, we give a necessary and sufficient condition for γ(β) = 1, i.e., that all rational numbers p/q ∈ [0, 1) with gcd(q, b) = 1 have a purely periodic β-expansion. A simple algorithm for determining the value of γ(β) for all quadratic Pisot numbers β is described.
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عنوان ژورنال:
- CoRR
دوره abs/1411.2419 شماره
صفحات -
تاریخ انتشار 2014