A convergence theorem for continued fractions
نویسندگان
چکیده
منابع مشابه
Duke’s Theorem and Continued Fractions
For uniformly chosen random α ∈ [0, 1], it is known the probability the nth digit of the continued-fraction expansion, [α]n converges to the Gauss-Kuzmin distribution P([α]n = k) ≈ log2(1 + 1/k(k + 2)) as n → ∞. In this paper, we show the continued fraction digits of √ d, which are eventually periodic, also converge to the Gauss-Kuzmin distribution as d → ∞ with bounded class number, h(d). The ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1940
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1940-0001320-1