Dessins d’Enfants, Their Deformations and Algebraic the Sixth Painlevé and Gauss Hypergeometric Functions
نویسنده
چکیده
We consider an application of Grothendieck’s dessins d’enfants to the theory of the sixth Painlevé and Gauss hypergeometric functions: two classical special functions of the isomonodromy type. It is shown that, higher order transformations and the Schwarz table for the Gauss hypergeometric function are closely related with some particular Belyi functions. Moreover, we introduce a notion of deformation of the dessins d’enfants and show that one dimensional deformations are a useful tool for construction of algebraic the sixth Painlevé functions. 2000 Mathematics Subject Classification: 34M55, 33E17, 33E30. Short title: Dessins d’Enfants and Algebraic Special Functions ∗E-mail: [email protected], [email protected]
منابع مشابه
Grothendieck’s Dessins D’enfants, Their Deformations, and Algebraic Solutions of the Sixth Painlevé and Gauss Hypergeometric Equations
Grothendieck’s dessins d’enfants are applied to the theory of the sixth Painlevé and Gauss hypergeometric functions, two classical special functions of isomonodromy type. It is shown that higher-order transformations and the Schwarz table for the Gauss hypergeometric function are closely related to some particular Bely̆ı functions. Moreover, deformations of the dessins d’enfants are introduced, ...
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