Grothendieck’s dessins d’enfants, their deformations, and algebraic solutions of the sixth Painlevé and Gauss hypergeometric equations
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- by A. V. Kitaev
- St. Petersburg Math. J. 17 (2006), 169-206
- DOI: https://doi.org/10.1090/S1061-0022-06-00899-5
- Published electronically: January 23, 2006
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Abstract:
Grothendieck’s dessins d’enfants are applied to the theory of the sixth Painlevé and Gauss hypergeometric functions, two classical special functions of iso- monodromy type. It is shown that higher-order transformations and the Schwarz table for the Gauss hypergeometric function are closely related to some particular Belyĭ functions. Moreover, deformations of the dessins d’enfants are introduced, and it is shown that one-dimensional deformations are a useful tool for construction of algebraic sixth Painlevé functions.References
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Bibliographic Information
- A. V. Kitaev
- Affiliation: St. Petersburg Branch, Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia, and School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia
- Email: kitaev@pdmi.ras.ru, kitaev@maths.usyd.edu.au
- Received by editor(s): September 25, 2003
- Published electronically: January 23, 2006
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 169-206
- MSC (2000): Primary 34M55, 33E17, 33E30
- DOI: https://doi.org/10.1090/S1061-0022-06-00899-5
- MathSciNet review: 2140681
Dedicated: Dedicated to Ludwig Dmitrievich Faddeev on the occasion of his 70th birthday