Limit theorems related to beta-expansion and continued fraction expansion
نویسندگان
چکیده
منابع مشابه
Beta-expansion and continued fraction expansion over formal Laurent series
Let x ∈ I be an irrational element and n 1, where I is the unit disc in the field of formal Laurent series F((X−1)), we denote by kn(x) the number of exact partial quotients in continued fraction expansion of x, given by the first n digits in the β-expansion of x, both expansions are based on F((X−1)). We obtain that lim inf n→+∞ kn(x) n = degβ 2Q∗(x) , lim sup n→+∞ kn(x) n = degβ 2Q∗(x) , wher...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2016
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.11.028