Algebraic independence of certain Mahler functions
Let \(K\) be a field of characteristic \(0\) and \(f \in Kz\) a solution of some Mahler functional equation. By work of Kubota and of Nishioka (see \textit{K. Nishioka} [Mahler functions and transcendence. Berlin: Springer (1996; Zbl 0876.11034)]) one has a criterion for the transcendence of \(f\), i.e., for \(f \not\in \overline{K(z)}\). The authors generalize it to a criterion for algebraic independence using an induction technique due to \textit{D. Duverney} [Math. Proc. Camb. Philos. Soc. 130, No. 2, 193--207 (2001; Zbl 0999.11037)]. Special cases of this criterion can be used to generalize a result by \textit{P. Bundschuh} and the second author [Bull. Aust. Math. Soc. 93, No. 3, 375--387 (2016; Zbl 1341.11042)].
scientific article; zbMATH DE number 6916264