On Particular Families of Hyperquadratic Continued Fractions in Power Series Fields of Odd Characteristic
Alain Lasjaunias
Institut de Mathématiques de Bordeaux
CNRS-UMR 5251
Université de Bordeaux
33405 Talence
France
Abstract:
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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