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

Alina Firicel. "Rational approximations to algebraic Laurent series with coefficients in a finite field." Acta Arithmetica 157.4 (2013): 297-322. <http://eudml.org/doc/279428>.

@article{AlinaFiricel2013,
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.},
author = {Alina Firicel},
journal = {Acta Arithmetica},
keywords = {automatic sequences; finite fields; irrationality measures; Laurent series; uniform morphisms},
language = {eng},
number = {4},
pages = {297-322},
title = {Rational approximations to algebraic Laurent series with coefficients in a finite field},
url = {http://eudml.org/doc/279428},
volume = {157},
year = {2013},
}

TY - JOUR
AU - Alina Firicel
TI - Rational approximations to algebraic Laurent series with coefficients in a finite field
JO - Acta Arithmetica
PY - 2013
VL - 157
IS - 4
SP - 297
EP - 322
AB - 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.
LA - eng
KW - automatic sequences; finite fields; irrationality measures; Laurent series; uniform morphisms
UR - http://eudml.org/doc/279428
ER -