# From a quartic continued fraction in $\mathbb{F}_3((T^-1))$ to a transcendental continued fraction in $\mathbb{Q}((T^-1))$ through an infinite word over {1,2}

2 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We explicitly describe a noteworthy transcendental continued fraction in the field of power series over Q, having irrationality measure equal to 3. This continued fraction is a generating function of a particular sequence in the set {1, 2}. 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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Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-01348576
Contributor : Nicolas Brisebarre <>
Submitted on : Wednesday, November 23, 2016 - 3:48:44 PM
Last modification on : Friday, April 20, 2018 - 3:44:26 PM
Document(s) archivé(s) le : Tuesday, March 21, 2017 - 10:34:16 AM

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W-bna2.pdf
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### Identifiers

• HAL Id : hal-01348576, version 2
• ARXIV : 1607.07235

### Citation

Bill Allombert, Nicolas Brisebarre, Alain Lasjaunias. From a quartic continued fraction in $\mathbb{F}_3((T^-1))$ to a transcendental continued fraction in $\mathbb{Q}((T^-1))$ through an infinite word over {1,2}. 2016. ⟨hal-01348576v2⟩

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