GENERALIZED PALINDROMIC CONTINUED FRACTIONS

In this paper, we introduce a generalization of palindromic continued fractions as studied by Adamczewski and Bugeaud [2]. We refer to these generalized palindromes as m-palindromes, where m ranges over the positive integers. We provide a simple transcendency criterion for m-palindromes, extending a...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2018-01, Vol.48 (1), p.219-236
Main Author: FREEMAN, DAVID M.
Format: Article
Language:English
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Summary:In this paper, we introduce a generalization of palindromic continued fractions as studied by Adamczewski and Bugeaud [2]. We refer to these generalized palindromes as m-palindromes, where m ranges over the positive integers. We provide a simple transcendency criterion for m-palindromes, extending and slightly refining an analogous result of Adamczewski and Bugeaud [2]. We also provide methods for constructing examples of m-palindromes. Such examples allow us to illustrate our transcendency criterion and to explore the relationship between m-palindromes and stammering continued fractions, another concept introduced by Adamczewski and Bugeaud.
ISSN:0035-7596
1945-3795
DOI:10.1216/RMJ-2018-48-1-219