Continued fractions and totally monotone sequences
نویسندگان
چکیده
منابع مشابه
Continued Fractions and Heavy Sequences
We initiate the study of the sets H(c), 0<c<1, of real x for which the sequence (kx)k≥1 (viewed mod 1) consistently hits the interval [0, c) at least as often as expected (i. e., with frequency ≥ c). More formally, H(c) def = {α ∈ R ∣ card({1 ≤ k ≤ n ∣ ⟨kα⟩ < c}) ≥ cn, for all n ≥ 1}, where ⟨x⟩ = x− [x] stands for the fractional part of x ∈ R. We prove that, for rational c, the sets H(c) are of...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1940
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1940-0002642-0