On the continued fraction expansion of the unique root in $\mathbb{F}_p$ of the equation $x^4+x^2-Tx-1/12=0$ and other related hyperquadratic expansions
Language
en
Article de revue
This item was published in
Finite Fields and Their Applications. 2012, vol. 18, n° 1, p. 26-34
Elsevier
English Abstract
In 1985, Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, he came across a particular equation of degree 4 in characteristic p=13. This ...Read more >
In 1985, Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, he came across a particular equation of degree 4 in characteristic p=13. This equation has an analogue for all primes p>=5. There are two patterns for the continued fraction of the solution of this equation, according to the residue of p modulo 3. We describe this pattern in the first case, considering especially p=7 and p=13. in the second case we only give indications.Read less <
English Keywords
Continued fractions
Fields of power series
Finite fields.
Finite fields
Origin
Hal imported