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.