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

Research paper by Tomasz Kisielewski

Indexed on: 09 Dec '15Published on: 09 Dec '15Published in: Mathematics - Number Theory



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.