On Lamé operators which are pull-backs of hypergeometric ones

Chiarellotto, Bruno

doi:10.1090/S0002-9947-1995-1308004-4

On Lamé operators which are pull-backs of hypergeometric ones
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Trans. Amer. Math. Soc. 347 (1995), 2753-2780 Request permission

Abstract:

We give a method that would allow one to calculate the number of Lamé operators, ${\mathcal {L}_n}$, $n \in {\mathbf {N}}$, with prescribed finite monodromy and do the calculation for the case $n = 1$. We find a bound for the degree over ${\mathbf {Q}}$ of the field of definition of the coefficients of a Lamé operator with prescribed finite monodromy and give examples of Lamé operators with finite monodromy. Finally we study Lamé operators with infinite monodromy and generic second order differential operators which are pull-backs of hypergeometric ones under algebraic maps.

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