Algebraic Independence by Approximation Method (II) |
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Authors: | Yaochen Zhu |
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Institution: | (1) Institute of Applied Mathematics, Academy of Mathematics and Systems Sciences, Academia Sinica, Beijing 100080, P. R. China Fax: 010-62541689, CN |
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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.
Received March 27, 1998, Accepted September 28, 1998 |
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Keywords: | Algebraic independence Continued fraction Approximation method |
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