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On a two-valued sequence and related continued fractions in power series fields

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Abstract

We explicitly describe a noteworthy transcendental continued fraction in the field of power series over \(\mathbb {Q}\), having irrationality measure equal to 3. This continued fraction is a generating function of a particular sequence in the set \(\lbrace 1,2\rbrace \). The origin of this sequence, whose study was initiated in a recent paper, is to be found in another continued fraction, in the field of power series over \(\mathbb {F}_3\), which satisfies a simple algebraic equation of degree 4, introduced thirty years ago by D. Robbins.

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Authors and Affiliations

  1. Institut de Mathématiques de Bordeaux CNRS-UMR 5251, Université de Bordeaux, 33405, Talence, France

    Bill Allombert & Alain Lasjaunias

  2. CNRS, Laboratoire LIP (CNRS, ENSL, Inria, UCBL), Université de Lyon, ENS Lyon, 46 Allée d’Italie, 69364, Lyon Cedex 07, France

    Nicolas Brisebarre

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  1. Bill Allombert
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  2. Nicolas Brisebarre
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  3. Alain Lasjaunias
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Correspondence to Alain Lasjaunias.

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Allombert, B., Brisebarre, N. & Lasjaunias, A. On a two-valued sequence and related continued fractions in power series fields. Ramanujan J 45, 859–871 (2018). https://doi.org/10.1007/s11139-017-9892-7

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  • DOI: https://doi.org/10.1007/s11139-017-9892-7

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