Algebraic solutions of the Lamé equation, revisited

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8 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)16-34
Number of pages19
JournalJournal of Differential Equations
Volume198
Issue number1
DOIs
StatePublished - Mar 20 2004

Keywords

  • Algebraic solution
  • Finite monodromy
  • Hypergeometric equation
  • Lamé equation
  • Projective monodromy group
  • Schwarz list

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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