Counting integral Lamé equations by means of dessins d’enfants
Counting integral Lamé equations by means of dessins d’enfants
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 $n \in \mathbb {Z}$ and $N \in \mathbb {N}$. This is done by performing the combinatorics of the 'dessins d'enfants' associated to …