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# Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic

Published:2013-01-10
Printed: Dec 2013
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 $$\alpha=\displaystyle\frac{A\alpha^{q}+B}{C\alpha^{q}}$$ 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
 MSC Classifications: 11J61 - Approximation in non-Archimedean valuations 11J70 - Continued fractions and generalizations [See also 11A55, 11K50]