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Diophantine Approximation for Certain Algebraic Formal Power Series in Positive Characteristic

  • K. Ayadi (a1), M. Hbaib (a1) and F. Mahjoub (a1)

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

$$\alpha =\frac{A{{\alpha }^{q}}+B}{C{{\alpha }^{q}}},$$

where $\left( A,B,C \right)\,\in \,{{\left( {{\mathbb{F}}_{q}}\left[ X \right] \right)}^{2}}\times \mathbb{F}_{q}^{*}\left[ X \right]$ . In particular, under some conditions on the polynomials $A,\,B$ and $C$ , we will give well approximated elements satisfying this equation.

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References

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