%0 Unpublished work
%T Diophantine properties of real numbers generated by finite automata
%+ Institut Camille Jordan (ICJ)
%+ Institut de mathématiques de Luminy (IML)
%A Adamczewski, Boris
%A Cassaigne, Julien
%8 2006-01-25
%D 2006
%Z math.NT/0601604
%K Diophantine approximation
%K Finite automata
%K irrationality measures
%Z 11J82, 11B85, 68R15
%Z Mathematics [math]/Number Theory [math.NT]Preprints, Working Papers, ...
%X We study some diophantine properties of automatic real numbers and we present a method to derive irrationality measures for such numbers. As a consequence, we prove that the $b$-adic expansion of a Liouville number cannot be generated by a finite automaton, a conjecture due to Shallit.
%G English
%2 https://hal.science/hal-00017758/document
%2 https://hal.science/hal-00017758/file/Adamczewski_Cassaigne.pdf
%L hal-00017758
%U https://hal.science/hal-00017758
%~ UNIV-ST-ETIENNE
%~ CNRS
%~ ICJ
%~ UNIV-AMU
%~ UNIV-LYON1
%~ INSA-LYON
%~ EC-LYON
%~ IML
%~ I2M
%~ INSA-GROUPE
%~ UDL
%~ UNIV-LYON