Algebraic Independence of Certain Generalized Mahler Type Numbers  

作　　者：Yao Chen ZHU 

机构地区：[1]Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R, China

出　　处：《Acta Mathematica Sinica,English Series》2007年第1期17-22,共6页数学学报（英文版）

基　　金：the NSFC(No.10571180)

摘　　要：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.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 

分 类 号：O15[理学—数学]