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

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• 作者：Tomasz Kisielewski ^{tomasz.kisielewski@uj.edu.pl}
• 关键词：Automatic sequence ; Regular sequence ; Mahler power series
• 刊名：Journal of Number Theory
• 出版年：2017
• 出版时间：May 2017
• 年：2017
• 卷：174
• 期：Complete
• 页码：456-486
• 全文大小：523 K
• 卷排序：174

文摘

Allouche and Shallit introduced the notion of a regular power series as a generalisation 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.