Geodesic
Rational approximations to algebraic Laurent series with coefficients in a finite field
Alina Firicel1
1 Institut Joseph Fourier Université de Grenoble 100 rue des maths, BP 74 38402 St Martin d'Hères Cedex, France
Acta Arithmetica, Tome 157 (2013) no. 4, pp. 297-322

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We give a general upper bound for the irrationality exponent of algebraic Laurent series with coefficients in a finite field. Our proof is based on a method introduced in a different framework by Adamczewski and Cassaigne. It makes use of automata theory and, in our context, of a classical theorem due to Christol. We then introduce a new approach which allows us to strongly improve this general bound in many cases. As an illustration, we give a few examples of algebraic Laurent series for which we are able to compute the exact value of the irrationality exponent.
DOI : 10.4064/aa157-4-1
Keywords: general upper bound irrationality exponent algebraic laurent series coefficients finite field proof based method introduced different framework adamczewski cassaigne makes automata theory context classical theorem due christol introduce approach which allows strongly improve general bound many cases illustration few examples algebraic laurent series which able compute exact value irrationality exponent

Alina Firicel 1

1 Institut Joseph Fourier Université de Grenoble 100 rue des maths, BP 74 38402 St Martin d'Hères Cedex, France 
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Alina Firicel. Rational approximations to algebraic Laurent
 series with coefficients in a finite field. Acta Arithmetica, Tome 157 (2013) no. 4, pp. 297-322. doi: 10.4064/aa157-4-1

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