Algebraic independence of certain Mahler numbers (Q2833087)

In this paper, the author proves algebraic independence results for the values of special degree \(1\) Mahler functions \(F(z)\) satisfying a functional equation of the form \(p(z)+p_0(z)F(z)+p_1(z)F(z^d)=0\) (\(d\geq 2\)), where \(p(z)\), \(p_0(z)\) and \(p_1(z)\) are polynomials with \(p_0(z)p_1(z)\neq 0\). In particular, the generating functions of Thue-Morse-Mahler, regular paper folding and Cantor sequences belong to this class, and the author obtains the algebraic independence of the values of these functions at every non-zero algebraic point in the open unit disk. This result is obtained from the more general result. The Mahler's method is used to prove the theorems.