Algebraic independence of certain Mahler numbers

2015/07/09 by Keijo Väänänen, Väänänen, Keijo
Mathematics · #11J81 #11J91 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J81 #msc:11J91

paper · pdf · doi:10.48550/arxiv.1507.02510

8 pages

arxiv created 2015/07/09 · arxiv updated 2015/07/10

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.

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