Algebraic Independence of Certain Generalized Mahler Type Numbers

Abstract

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 \( M_{{h_{i} }} {\left( {g_{i} ;A,T} \right)}{\left( {1 \leqslant i \leqslant s} \right)} \) 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.