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} - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2016

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}

Résumé

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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Dates et versions

hal-01348576 , version 1 (25-07-2016)
hal-01348576 , version 2 (23-11-2016)
hal-01348576 , version 3 (14-03-2017)

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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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