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Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic

  Published:2013-01-10
 Printed: Dec 2013
  • 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.
Keywords: diophantine approximation, formal power series, continued fraction diophantine approximation, formal power series, continued fraction
MSC Classifications: 11J61, 11J70 show english descriptions Approximation in non-Archimedean valuations
Continued fractions and generalizations [See also 11A55, 11K50]
11J61 - Approximation in non-Archimedean valuations
11J70 - Continued fractions and generalizations [See also 11A55, 11K50]
 

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