Counting Integral Lamé Equations by Means of Dessins d'Enfants

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We obtain an explicit formula for the number of Lamé equations (modulo scalar equivalence) with index $n$ and projective monodromy group of order $2N$, for given $n \in \Z$ and $N \in \N$. 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.
with 9 figures

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Classical Analysis and ODEs, 12H20; 34L40, 34M15

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http://salesiana.dossiersoluciones.com/handle/123456789/69382

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0311510
 http://arxiv.org/abs/math/0311510

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arXiv