Arithmetic properties of solutions of certain functional equations in several variables (Q1864851)

This is a generalization to several variables of the paper [Math. Ann. 325, 123--136 (2003; Zbl 1025.11023)] of the second author. As an application a measure of linear independence for a linear form in the values at some rational points of the function \[ f(z)=\sum^\infty_{n=0} \left(\prod^n_{ k=1} A(k)\right)^{-1} z^n \] is given. Here the sequence \(A(k)\), \(k=1,2,\dots,\) satisfies a certain linear recurrence.