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Counting Integral Lamé Equations by Means of Dessins d'Enfants

Sander Dahmen
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Abstract

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.

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Sander Dahmen. 2003-11-27. Counting Integral Lamé Equations by Means of Dessins d'Enfants. https://arxiv.org/abs/math/0311510

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