Algebraic Solutions of the Lamé Equation, Revisited
| dc.creator | Maier, Robert S. | |
| dc.date | 2002-06-26 | |
| dc.date.accessioned | 2026-07-07T04:49:24Z | |
| dc.date.available | 2026-07-07T04:49:24Z | |
| dc.description | 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. | |
| dc.description | 20 pages, elsart document class, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0206285 | |
| dc.identifier | http://arxiv.org/abs/math/0206285 | |
| dc.identifier | J. Differential Equations 198 (2004) 16-34. | |
| dc.identifier | doi:10.1016/j.jde.2003.06.006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64410 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 34A20 (Primary) 33E10,14H05 (Secondary) | |
| dc.title | Algebraic Solutions of the Lamé Equation, Revisited | |
| dc.type | text |