کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4593534 1630656 2016 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On a problem of countable expansions
ترجمه فارسی عنوان
در یک مسئله گسترش قابل شمارش
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

For a real number q∈(1,2)q∈(1,2) and x∈[0,1/(q−1)]x∈[0,1/(q−1)], the infinite sequence (di)(di) is called a q-expansion of x ifx=∑i=1∞diqi,di∈{0,1}for all i≥1. For m=1,2,⋯m=1,2,⋯ or ℵ0ℵ0 we denote by BmBm the set of q∈(1,2)q∈(1,2) such that there exists x∈[0,1/(q−1)]x∈[0,1/(q−1)] having exactly m different q-expansions. It was shown by Sidorov [18] that q2:=min⁡B2≈1.71064q2:=min⁡B2≈1.71064, and later asked by Baker [1] whether q2∈Bℵ0q2∈Bℵ0? In this paper we provide a negative answer to this question and conclude that Bℵ0Bℵ0 is not a closed set. In particular, we give a complete description of x∈[0,1/(q2−1)]x∈[0,1/(q2−1)] having exactly two different q2q2-expansions.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Number Theory - Volume 158, January 2016, Pages 134–150
نویسندگان
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