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Sur l'irréductibilité dans l'anneau des séries de Dirichlet analytiques.

Frédéric Bayart, Augustin Mouze (2005)

Publicacions Matemàtiques

We discuss some local analytic properties of the ring of Dirichlet series. We obtain mainly the equivalence between the irreducibility in the analytic ring and in the formal one. In the same way we prove that the ring of analytic Dirichlet series is integrally closed in the ring of formal Dirichlet series. Finally we introduce the notion of standard basis in these rings and we give a finitely generated ideal which does not admit standard bases.

Théorème de division et stabilité en géométrie analytique locale

André Galligo (1979)

Annales de l'institut Fourier

À l’aide d’un théorème de division de séries entières convergentes avec estimation des normes sur un système fondamental de polydisques, on démontre un théorème de “passage du formel au convergent”. Ceci nous permet d’étudier les morphismes stables et plats entre germes d’espaces analytiques singuliers.

Théorème de préparation pour les fonctions logarithmico-exponentielles

Jean-Marie Lion, Jean-Philippe Rolin (1997)

Annales de l'institut Fourier

Nous donnons une preuve géométrique du théorème d’élimination des quantificateurs pour les fonctions logarithmico-exponentielles prouvé initialement par van den Dries, Macintyre et Marker. Notre démonstration n’utilise pas de Théorie des Modèles. Elle repose sur un théorème de préparation pour les fonctions sous-analytiques.

Théorèmes de préparation Gevrey et étude de certaines applications formelles

Augustin Mouze (2003)

Annales Polonici Mathematici

We consider subrings A of the ring of formal power series. They are defined by growth conditions on coefficients such as, for instance, Gevrey conditions. We prove preparation theorems of Malgrange type in these rings. As a consequence we study maps F from ℂ s to ℂ p without constant term such that the rank of the Jacobian matrix of F is equal to 1. Let be a formal power series. If F is a holomorphic map, the following result is well known: ∘ F is analytic implies there exists a convergent power series...

Weierstrass division theorem in quasianalytic local rings

Abdelhafed Elkhadiri, Hassan Sfouli (2008)

Studia Mathematica

The main result of this paper is the following: if the Weierstrass division theorem is valid in a quasianalytic differentiable system, then this system is contained in the system of analytic germs. This result has already been known for particular examples, such as the quasianalytic Denjoy-Carleman classes.

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