摘要
Let f（x）be a continued fraction with elements a<sub>n</sub>x,where coefficients a<sub>n</sub> are positive alge- braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers α<sub>1</sub>,...,α<sub>s</sub> with distinct absolute values the algebraic independence of the values f（α<sub>1</sub>）,...,f（α<sub>s</sub>）is proved under certain as- sumption concerning only with a<sub>n</sub>.For some transcendental numbers ζ the algebraic independence of values f（ζ<sup>j</sup>）（j∈Z）is also established.
Let f（x）be a continued fraction with elements a<sub>n</sub>x,where coefficients a<sub>n</sub> are positive alge- braic numbers.Using the criterion of[1]for any nonzero real algebraic numbers α<sub>1</sub>,...,α<sub>s</sub> with distinct absolute values the algebraic independence of the values f（α<sub>1</sub>）,...,f（α<sub>s</sub>）is proved under certain as- sumption concerning only with a<sub>n</sub>.For some transcendental numbers ζ the algebraic independence of values f（ζ<sup>j</sup>）（j∈Z）is also established.
基金
Supported by the National Natural Science Foundation of China
