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Rational approximations to algebraic Laurent series with coefficients in a finite field

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Firicel A.

Acta Arithmetica

2013

tom 157

nr 4

297-322

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.

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1 Acta Arithmetica

1 Firicel A.

1 2013

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Rational approximations to algebraic Laurent series with coefficients in a finite field