Geodesic
Diophantine Approximation for CertainAlgebraic Formal Power Series in PositiveCharacteristic
Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 673-683

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DOI

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.
DOI : 10.4153/CMB-2012-041-2
Mots-clés : 11J61, 11J70, diophantine approximation, formal power series, continued fraction 
Ayadi, K.; Hbaib, M.; Mahjoub, F. Diophantine Approximation for CertainAlgebraic Formal Power Series in PositiveCharacteristic. Canadian mathematical bulletin, Tome 56 (2013) no. 4, pp. 673-683. doi: 10.4153/CMB-2012-041-2
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     title = {Diophantine {Approximation} for {CertainAlgebraic} {Formal} {Power} {Series} in {PositiveCharacteristic}},
     journal = {Canadian mathematical bulletin},
     pages = {673--683},
     year = {2013},
     volume = {56},
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     doi = {10.4153/CMB-2012-041-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-041-2/}
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