http://dx.doi.org/10.4153/CMB-2012-041-2
10 pages
Published:2013-01-10
K. Ayadi, Université de Sfax, Faculté des Sciences, Département de Mathématiques, BP 802, 3038 Sfax, Tunisie M. Hbaib, Université de Sfax, Faculté des Sciences, Département de Mathématiques, BP 802, 3038 Sfax, Tunisie F. Mahjoub, Université de Sfax, Faculté des Sciences, Département de Mathématiques, BP 802, 3038 Sfax, Tunisie
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Abstract
In this paper, we study rational approximations for certain algebraic power series over a finite field.
We obtain results for irrational elements of strictly positive degree
satisfying an equation of the type
\begin{equation}
\alpha=\displaystyle\frac{A\alpha^{q}+B}{C\alpha^{q}}
\end{equation}
where $(A, B, C)\in
(\mathbb{F}_{q}[X])^{2}\times\mathbb{F}_{q}^{\star}[X]$.
In particular,
we will give, under some conditions on the polynomials $A$, $B$
and $C$, well approximated elements satisfying this equation.
© Canadian Mathematical Society, 2013
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