- Title
- Mahler takes a regular view of Zaremba
- Creator
- Coons, Michael
- Relation
- ARC.DE140100223 http://purl.org/au-research/grants/arc/DE140100223
- Relation
- Integers Vol. 18A, no. A6
- Relation
- http://math.colgate.edu/~integers/vol18a.html
- Publisher
- Integers
- Resource Type
- journal article
- Date
- 2018
- Description
- In the theory of continued fractions, Zaremba's conjecture states that there is a positive integer M such that each integer is the denominator of a convergent of an ordinary continued fraction with partial quotients bounded by M. In this paper, to each such M we associate a regular sequence---in the sense of Allouche and Shallit---and establish various properties and results concerning the generating function of the regular sequence. In particular, we determine the minimal algebraic relation concerning the generating function and its Mahler iterates.
- Subject
- continued fractions; Mahler iterates; minimal algebraic relation; generating function
- Identifier
- http://hdl.handle.net/1959.13/1466738
- Identifier
- uon:47643
- Identifier
- ISSN:1553-1732
- Language
- eng
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