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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-1,
author = {Alina Firicel},
title = {Rational approximations to algebraic Laurent series with coefficients in a finite field},
journal = {Acta Arithmetica},
volume = {161},
year = {2013},
pages = {297-322},
zbl = {1291.11098},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-1}
}
Alina Firicel. Rational approximations to algebraic Laurent series with coefficients in a finite field. Acta Arithmetica, Tome 161 (2013) pp. 297-322. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa157-4-1/