Algebraic solutions of the Lamé equation, revisited |
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Authors: | Robert S Maier |
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Institution: | a Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA b Department of Physics, University of Arizona, Tucson, AZ 85721, USA |
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Abstract: | A minor error in the necessary conditions for the algebraic form of the Lamé equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out (see Baldassarri, J. Differential Equations 41 (1) (1981) 44). It is shown that if the group is the octahedral group S4, then the degree parameter of the equation may differ by ±1/6 from an integer; this possibility was missed. The omission affects a recent result on the monodromy of the Weierstrass form of the Lamé equation (see Churchill, J. Symbolic Comput. 28 (4-5) (1999) 521). The Weierstrass form, which is a differential equation on an elliptic curve, may have, after all, an octahedral projective monodromy group. |
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Keywords: | 34A20 33E10 14H05 |
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