#### Alladi Ramakrishnan Hall

#### Mahler method and Galois theory

#### P. PHILIPPON

##### University of Paris VI

*Mahler method gives good lower bounds for the transcendence degree of fields generated by values of functions *

satisfying functional equations. We show how Galois theory of this type of equations leads to a refinement of these results, bringing

Mahler theory for algebraic independence in a similar state as $E$-functions theory.

Done