Lamé方程的代数解
Algebraic Solutions of the Lamé Equation, Revisited
摘要：
一个小错误的必要条件的代数形式的拉梅方程有一个有限的投影monodromy组，因此，它只有代数的解决方案，指出。[See F. Baldassarri，“On algebraic solutions of Lamé's differential equation“，J.微分方程41（1981），44-58.]证明了如果群是八面体群S_4，则方程的度参数可能与整数相差+1/6或-1/6，这种可能性被忽略了。遗漏影响最近的结果单值的维尔斯特拉斯形式的拉梅方程。[See R. C. Churchill，“SL（2，C）的双生成子群和超几何、黎曼和拉梅方程”，J.符号计算28（1999），521-545.]维尔斯特拉斯形式是椭圆曲线上的一个微分方程，它毕竟可以有一个八面体射影单值群。
英文摘要：
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 F. Baldassarri, "On algebraic solutions of Lamé's differential equation", J. Differential Equations 41 (1981), 44-58.] It is shown that if the group is the octahedral group S_4, then the degree parameter of the equation may differ by +1/6 or -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 R. C. Churchill, "Two-generator subgroups of SL(2,C) and the hypergeometric, Riemann, and Lamé equations", J. Symbolic Computation 28 (1999), 521-545.] 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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