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algebraic independence of Certain Numbers

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Acta Mathematica Sinica,English Series 1999年第4期15卷 507-514页

作者： Yonggao Chen Department of Mathematics,Nanjing Normal University,Nanjing 210097,P.R.ChinaYaochen Zhu Institute of Applied Mathematics,Academia Sinica,Beijing 100080,P.R.China Department of Mathematics Nanjing Normal University Nanjing P. R. China Institute of Applied Mathematics Academia Sinica Beijing P. R. China

In this note the algebraic independence of values of general Mahler series with different parameters at algebraic points is established.

关键词： algebraic independence General Mahler series Continued fraction

algebraic independence by Approximation Method(Ⅱ)

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Acta Mathematica Sinica,English Series 2000年第3期16卷 395-398页

作者： Yaochen Zhu Institute of Applied Mathematics,Academy of Mathematics and Systems Sciences,Academia Sinica,Beijing 100080,P.R.China Fax:010-62541689 Institute of Applied Mathematics Academy of Mathematics and Systems Sciences Academia Sinica Beijing 100080 P. R. China

Let f（x）be a continued fraction with elements anx,where coefficients an are positive alge- braic *** the criterion of[1]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 as- sumption concerning only with an.For some transcendental numbers ζ the algebraic independence of values f（ζj）（j∈Z）is also established.

关键词： algebraic independence Continued fraction Approximation method

algebraic independence by Approximation Method

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Acta Mathematica Sinica,English Series 1998年第3期14卷 295-302页

作者： Zhu Yaochen Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China Institute of Applied Mathematics Academia Sinica

By the use of approximation method a general criterion of algebraic independence of complex numbers is established. As its application the algebraic independence of values of certain gap series at algebraic and transc... 详细信息

关键词： algebraic independence Approximation method Gap series

algebraic independence of Certain Generalized Mahler Type Numbers

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Acta Mathematica Sinica,English Series 2007年第1期23卷 17-22页

作者： Yao Chen ZHU Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 P. R China

In this paper the generalized Mahler type number Mh（g;A,T） is defined, and in the case of multiplicatively dependent parameters gi, hi（1 ≤ i ≤ s） the algebraic independence of the numbers Mhi （gi; A, T）（1 ≤ i ≤ s） is proved, where A and T are certain infinite sequences of non-negative integers and of positive integers, respectively. Furthermore, the algebraic independence result on values of a certain function connected with the generalized Mahler type number and its derivatives at algebraic numbers is also given.

关键词： Mahler type numbers Generalized Mahler type numbers algebraic independence Multiplicative dependence

algebraic independence of values of certain Fourier series

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Science China Mathematics 2001年第6期44卷 718-726页

作者：朱尧辰 Chinese Acad Sci Chinese Acad Math & Syst Sci Inst Appl Math Beijing 100080 Peoples R China

The algebraic independence of values of certain Fourier series with algebraic coefficients and their derivatives at algebraic points is proved.

关键词： algebraic independence Fourier series algebraic points.

An Arithmetic Property of Mahler's Series

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Acta Mathematica Sinica,English Series 1997年第3期13卷 407-412页

作者： Zhu Yaochen (Institute of Applied Mathematics,Academia Sinica,Beijing 100080,China) Institute of Applied Mathematics Academia Sinica

In the present note the algebraic independence of values of several Mahler series with certain particular and different parameters at algebraic points is established by means of a typical approximation method handling... 详细信息

关键词： algebraic independence Mahler’s series Approximation method