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1. CMB 2013 (vol 56 pp. 673)

Ayadi, K.; Hbaib, M.; Mahjoub, F.
Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic
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.

Keywords:diophantine approximation, formal power series, continued fraction
Categories:11J61, 11J70

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