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Algebraic Independence of Certain Generalized Mahler Type Numbers

# Algebraic Independence of Certain Generalized Mahler Type Numbers,10.1007/s10114-005-0766-3,Acta Mathematica Sinica-english Series,Yao Chen Zhu

Algebraic Independence of Certain Generalized Mahler Type Numbers
In this paper the generalized Mahler type number M h (g; A, T) is defined, and in the case of multiplicatively dependent parameters gi, hi(1 ≤ i ≤ s) the algebraic independence of the numbers $$M_{{h_{i} }} {\left( {g_{i} ;A,T} \right)}{\left( {1 \leqslant i \leqslant s} \right)}$$ 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.