Algebraic solutions of the Lame equation, revisited.

A minor error in the necessary conditions for the algebraic form of the Lame 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 S-4, 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 Lame 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. (C) 2003 Elsevier Inc. All rights reserved.