Mahler takes a regular view of Zaremba

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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