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

DOI:
https://doi.org/10.1090/S0002-9947-1995-1308004-4

MathSciNet review:
1308004

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Abstract: We give a method that would allow one to calculate the number of Lamé operators, , , with prescribed finite monodromy and do the calculation for the case . We find a bound for the degree over 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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DOI:
https://doi.org/10.1090/S0002-9947-1995-1308004-4

Article copyright:
© Copyright 1995
American Mathematical Society