On Lamé operators which are pull-backs of hypergeometric ones

Chiarellotto, Bruno

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

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ISSN 1088-6850(online) ISSN 0002-9947(print)

On Lamé operators which are pull-backs of hypergeometric ones

Author: Bruno Chiarellotto
Journal: Trans. Amer. Math. Soc. 347 (1995), 2753-2780
MSC: Primary 34A20; Secondary 14E20, 14H30, 30F40, 34B30
MathSciNet review: 1308004
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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 . 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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