Séminaires : Géométrie et Théorie des Modèles

O-minimality has been used to prove functional transcendence results for important periodic functions like exponentiation and the j function. The Gamma function, which is not periodic but which satisfies simple functional equations, is definable in an o-minimal structure when restricted to certain unbounded regions in the complex plane. In the first part of the talk, I will present work with P. Speissegger on definable holomorphic continuations of functions definable in two particular o-minimal structures, with an application to definability of the complex Gamma function. Then I will discuss some functional transcendence properties of the Gamma function.