Fourth order linear differential equations with imprimitive group

ABSTRACT

In this paper we study fourth order linear differential equations whose differential Galois groups are imprimitive. We derive optimal bounds for the degree of the minimal polynomial of the logarithmic derivative of a Liouvillian solution. This is the lowest possible order where imprimitive non monomial groups occur.

REFERENCES

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION

Additional Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.2 Algorithms

General Terms:
Algorithms, Theory