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Diophantine Approximation for CertainAlgebraic Formal Power Series in PositiveCharacteristic
Published online by Cambridge University Press: 20 November 2018
Abstract.
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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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