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Diophantine Approximation for CertainAlgebraic Formal Power Series in PositiveCharacteristic

Published online by Cambridge University Press:  20 November 2018

K. Ayadi ,
M. Hbaib  and
F. Mahjoub
K. Ayadi
Affiliation:
Université de Sfax, Faculté des Sciences, Département de Mathématiques, BP 802, 3038 Sfax, Tunisie e-mail: [email protected]@[email protected]
M. Hbaib
Affiliation:
Université de Sfax, Faculté des Sciences, Département de Mathématiques, BP 802, 3038 Sfax, Tunisie e-mail: [email protected]@[email protected]
F. Mahjoub
Affiliation:
Université de Sfax, Faculté des Sciences, Département de Mathématiques, BP 802, 3038 Sfax, Tunisie e-mail: [email protected]@[email protected]
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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.

Keywords

11J6111J70diophantine approximationformal power seriescontinued fraction
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 673 - 683
Copyright
Copyright © Canadian Mathematical Society 2013

References

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