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Any algebraic (resp. linear) relation over the field of rational functions with algebraic coefficients between given analytic functions leads by specialization to algebraic (resp. linear) relations over the field of algebraic numbers between the values of these functions. Number theorists have long been interested in proving results going in the other direction. Though the converse result is known to be false in general, Mahler’s method provides one of the few known instances where it essentially holds true. After the works of Nishioka, and more recently of Philippon, Faverjon and the speaker, the theory of Mahler functions in one variable is now rather well understood. In contrast, and despite the contributions of Mahler, Loxton and van der Poorten, Kubota, Masser, and Nishioka among others, the theory of Mahler functions in several variables remains much less developed. In this talk, I will discuss recent progresses concerning the case of regular singular systems, as well as possible applications of this theory. This is a joint work with Colin Faverjon. Any algebraic (resp. linear) relation over the field of rational functions with algebraic coefficients between given analytic functions leads by specialization to algebraic (resp. linear) relations over the field of algebraic numbers between the values of these functions. Number theorists have long been interested in proving results going in the other direction. Though the converse result is known to be false in general, Mahler’s method provides ...

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Documents 11J81 | enregistrements trouvés : 37

Mahler's method in several variables Adamczewski, Boris | CIRM H Nouveau

Cinquante ans de polynomes. fifty years of polynomialsproceedings od a conference held in honour of alain durand at the institut henri poincare,paris,france,may 26- 27,1988 Langevin, M. ; Waldschmidt, M. | Springer-Verlag 1990 Nouveau

Séminaire d'arithmétique année 1990-91-92 | Faculté de Sciences et Techniques Université de Saint-Etienne 1992 Nouveau

Journées arithmétiques de Bordeaux :Mai 27 - Juin 1 | Société Mathématique de France 1975 Nouveau

Rencontres arithmétiques de Caenles retombéesà la mémoire du Professeur Roger ApéryJuin 2-3 | Universite De Caen 1985 Nouveau

Séminaire de théorie des nombres 1970-1971 | Laboratoire de théorie des nombres 1970 Nouveau

Irrationalzahlen Perron, Oskar | Walter De Gruyter & Co. 1947 Nouveau

Linear forms in logarithms and applications Bugeaud, Yann | European Mathematical Society 2018 Nouveau

Vorlesungen über die theorie der algebraischen zahlen Hecke, Erich | Akademische Verlagsgesellschaft 1923 Nouveau

Diophantische approximationen Koksma, J. F. | Chelsea Publishing Co. 1936 Nouveau

Transcendental numbers Lipman, Joseph | Queen'S University 1966 Nouveau

Lectures on diophantine approximation. Part. I :g-adic numbers and Roth's theorem Mahler, Kurt | Cushing-Malloy, Inc. 1961 Nouveau

Einführung in die transzendenten zahlen Schneider, Th. | Springer-Verlag 1957 Nouveau

Introduction aux nombres transcendants Schneider, Dr. Théodor | Gauthier-Villars 1959 Nouveau

Transcendental numbers Siegel, Carl Ludwig | Princeton University Press 1949 Nouveau

Transcendence methods Waldschmidt, Michel | Queen'S University 1979 Nouveau

Lehrbuch der algebra Vol. II Weber, Heinrich | Chelsea Publishing Co. 9999 Nouveau

Lehrbuch der algebra. Vol. II Weber, Heinrich | Druck und Verlag von Friedrich Vieweg & Sons 1899 Nouveau

Mathematische Abhandlungen :besonders aus dem Gebiete der höheren Arithmetik und der elliptischen Funnktionen Eisenstein, G. ; Gauss, C. F. | Georg Olms Verlagsbuchhandlung 1967 Nouveau

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Cinquante ans de polynomes. fifty years of polynomials
proceedings od a conference held in honour of alain durand at the institut henri poincare,paris,france,may 26- 27,1988 Langevin, M. ; Waldschmidt, M. | Springer-Verlag 1990 Nouveau

Journées arithmétiques de Bordeaux :
Mai 27 - Juin 1 | Société Mathématique de France 1975 Nouveau

Rencontres arithmétiques de Caen
les retombées
à la mémoire du Professeur Roger Apéry
Juin 2-3 | Universite De Caen 1985 Nouveau

Lectures on diophantine approximation. Part. I :
g-adic numbers and Roth's theorem Mahler, Kurt | Cushing-Malloy, Inc. 1961 Nouveau

Mathematische Abhandlungen :
besonders aus dem Gebiete der höheren Arithmetik und der elliptischen Funnktionen Eisenstein, G. ; Gauss, C. F. | Georg Olms Verlagsbuchhandlung 1967 Nouveau