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

### Volume 157 / 2013

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

#### Abstract

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.