Abstract
Let f (x) be a continued fraction with elements a n x, where coefficients a n are positive algebraic numbers. Using the criterion of [l] for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the algebraic independence of the values f(α1), ..., f(αs) is proved under certain assumption concerning only with a n . For some transcendental numbers ξ the algebraic independence of values f(ξj)(j∈ℤ) is also established.
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Supported by the National Natural Science Foundation of China
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Zhu, Y. Algebraic Independence by Approximation Method (II). Acta Math Sinica 16, 395–398 (2000). https://doi.org/10.1007/s101140000076
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DOI: https://doi.org/10.1007/s101140000076