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Fast growing sequences of partial denominators. (English) Zbl 0856.11034

Let \(a=[0,a_1,a_2,\dots]\) \((a_n\in\mathbb{N})\) be a continued fraction and \(q_n\) be a denominator of its partial fraction. Suppose there exist \(s\in\mathbb{N}\), \(K>0\) and a strictly increasing sequence \(\{n_j\}\) of positive integers such that \(q_{n_j}<a^K_{n_j}\). Then the number \(a\) is transcendental.
Reviewer: J.Hančl (Ostrava)

MSC:

11J70 Continued fractions and generalizations
11J82 Measures of irrationality and of transcendence
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References:

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