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- W1825284657 abstract "For a real number q∈(1,2) and x∈[0,1/(q−1)], the infinite sequence (di) is called a q-expansion of x ifx=∑i=1∞diqi,di∈{0,1}for alli≥1. For m=1,2,⋯ or ℵ0 we denote by Bm the set of q∈(1,2) such that there exists x∈[0,1/(q−1)] having exactly m different q-expansions. It was shown by Sidorov [18] that q2:=minB2≈1.71064, and later asked by Baker [1] whether q2∈Bℵ0? In this paper we provide a negative answer to this question and conclude that Bℵ0 is not a closed set. In particular, we give a complete description of x∈[0,1/(q2−1)] having exactly two different q2-expansions." @default.
- W1825284657 created "2016-06-24" @default.
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- W1825284657 date "2016-01-01" @default.
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- W1825284657 title "On a problem of countable expansions" @default.
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- W1825284657 doi "https://doi.org/10.1016/j.jnt.2015.06.017" @default.
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