Some functional transcendence results around the Schwarzian differential equation.

Blázquez-Sanz, David; Casale, Guy; Freitag, James; Nagloo, Joel

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1265-1300.

Dans cet article, nous démontrons des variantes du théorème d’Ax–Lindemann–Weierstrass (ALW) pour des fonctions analytiques satisfaisant des équations différentielles de type « Schwarzienne ». Dans des travaux antérieurs, nous avons prouvé le théorème ALW pour les uniformisantes de groupes fuchsiens de genre zéro. Dans ce travail, nous généralisons ce résultat de plusieurs manières en utilisant des techniques variées provenant de la théorie des modèles, de la théorie de Galois différentielle et de la géométrie complexe.

This paper centers around proving variants of the Ax–Lindemann–Weierstrass (ALW) theorem for analytic functions which satisfy Schwarzian differential equations. In previous work, the authors proved the ALW theorem for the uniformizers of genus zero Fuchsian groups, and in this work, we generalize that result in several ways using a variety of techniques from model theory, differential Galois theory and complex geometry.

Classification : 11F03, 12H05, 03C60

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