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

Volume 157 / 2013

Alina Firicel Acta Arithmetica 157 (2013), 297-322 MSC: 11J61, 11J82, 11T99, 68R15. DOI: 10.4064/aa157-4-1


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.


  • Alina FiricelInstitut Joseph Fourier
    Université de Grenoble
    100 rue des maths, BP 74
    38402 St Martin d'Hères Cedex, France

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