Journal of Integer Sequences, Vol. 21 (2018), Article 18.8.3

On Particular Families of Hyperquadratic Continued Fractions in Power Series Fields of Odd Characteristic

Alain Lasjaunias
Institut de Mathématiques de Bordeaux
Université de Bordeaux
33405 Talence


We discuss the form of certain algebraic continued fractions in the field of power series over Fp, where p is an odd prime number. This leads to giving explicit continued fractions in these fields, satisfying an explicit algebraic equation of arbitrary degree d ≥ 2 and having an irrationality measure equal to d. Our results are based on a mysterious finite sequence of rational numbers.

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Received March 8 2018; revised version received September 12 2018; November 4 2018. Published in Journal of Integer Sequences, November 24 2018.

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