Algebraic independence of certain Mahler numbers

TL;DR

This paper proves algebraic independence of values of certain Mahler functions, including those related to Thue-Morse, paperfolding, and Cantor sequences, at all non-zero algebraic points inside the unit disk, using Mahler's method.

Contribution

It establishes algebraic independence results for a class of Mahler functions, including well-known sequence generating functions, at algebraic points.

Findings

Values of Mahler functions at algebraic points are algebraically independent.

Includes functions related to Thue-Morse, paperfolding, and Cantor sequences.

Uses Mahler's method to prove independence.

Abstract

In this note we prove algebraic independence results for the values of a special class of Mahler functions. In particular, the generating functions of Thue-Morse, regular paperfolding and Cantor sequences belong to this class, and we obtain the algebraic independence of the values of these functions at every non-zero algebraic point in the open unit disk. The proof uses results on Mahler's method.