Counting Integral Lamé Equations by Means of Dessins D’enfants
نویسنده
چکیده
We obtain an explicit formula for the number of Lamé equations (modulo linear changes of variable) with index n and projective monodromy group of order 2N , for given n ∈ Z and N ∈ N. This is done by performing the combinatorics of the ‘dessins d’enfants’ associated to the Belyi covers which transform hypergeometric equations into Lamé equations by pull-back.
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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تاریخ انتشار 2006