Algebraic independence of certain Mahler numbers

作者：Vaananen Keijo^*

来源：International Journal of Number Theory, 2016, 12(8): 2159-2166.

DOI：10.1142/S1793042116501293

• Algebraic independence of numbers
• Mahler's method
• Thue-Morse-Mahler numbers
• regular paperfolding numbers

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 paper-folding 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.

• 出版日期2016-12