On Particular Families of Hyperquadratic Continued Fractions in Power Series Fields of Odd Characteristic
Institut de Mathématiques de Bordeaux
Université de Bordeaux
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.
Full version: pdf,
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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