Criteria for regularity of Mahler power series and Becker's conjecture

2015/12/09 by Tomasz Kisielewski, Kisielewski, Tomasz
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1512.04326

arxiv created 2015/12/09 · arxiv updated 2015/12/15

Abstract

Allouche and Shallit introduced the notion of a regular power series as a generalization of automatic sequences. Becker showed that all regular power series satisfy Mahler equations and conjectured equivalent conditions for the converse to be true. We prove a stronger form of Becker's conjecture for a subclass of Mahler power series.

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