Some functional transcendence results around the Schwarzian differential equation.
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 5, pp. 1265-1300.

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.

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.

Published online:
DOI: 10.5802/afst.1661
Classification: 11F03, 12H05, 03C60
Blázquez-Sanz, David 1; Casale, Guy 2; Freitag, James 3; Nagloo, Joel 4

1 Universidad Nacional de Colombia - Sede Medellín, Facultad de Ciencias, Escuela de Matemáticas, Colombia
2 Univ Rennes, CNRS, IRMAR-UMR 6625, F-35000 Rennes, France
3 University of Illinois Chicago, Department of Mathematics, Statistics, and Computer Science, 851 S. Morgan Street, Chicago, IL, USA, 60607-7045.
4 CUNY Bronx Community College, Department of Mathematics and Computer Science, Bronx, NY 10453, and CUNY Graduate Center, Ph.D. programs in Mathematics, 365 Fifth Avenue, New York, NY 10016, USA
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Blázquez-Sanz, David; Casale, Guy; Freitag, James; Nagloo, Joel. Some functional transcendence results around the Schwarzian differential equation.. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 5, pp. 1265-1300. doi : 10.5802/afst.1661. http://www.numdam.org/articles/10.5802/afst.1661/

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