Original scientific paper
Diophantine approximation for the cubic root of polynomials of $\mathbb{F}_{2}[X]$
Khalil Ayadi
; Département de mathématiques, Faculté des sciences, Université de Sfax, Sfax, Tunisie
Mohamed Hbaib
; Département de mathématiques, Faculté des sciences, Université de Sfax, Sfax, Tunisie
Faiza Mahjoub
; Département de mathématiques, Faculté des sciences, Université de Sfax, Sfax, Tunisie
Abstract
In this paper, with different approaches we study rational
approximation for the algebraic {formal power series} in
$\mathbb{F}_{2}((X^{-1}))$ solving the irreducible equation
\[\alpha^{3}=R,\]
where $R$ is a polynomial of $\mathbb{F}_{2}[X]$.
Moreover, for some polynomials $R$, we give explicitly the
continued fraction expansion of the root of this equation.
Keywords
finite field; formal power series; continued fraction expansion
Hrčak ID:
93295
URI
Publication date:
5.12.2012.
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