On linear differential equations with reductive Galois group

Malagón, Camilo Sanabria

doi:10.1016/j.jalgebra.2014.02.035

Cited by 3 publications

(6 citation statements)

References 17 publications

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“…The present paper is mainly concerned with (i). It clarifies and extends work of [Ber,S1,S2,S3]. Moreover we propose new methods and examples for (i) related to a theorem of Compoint [C, B] concerning invariants.…”

Section: Introductionmentioning

confidence: 57%

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Linear differential equations with finite differential Galois group

2020

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For a differential operator L of order n over C(z) with a finite (differential) Galois group G ⊂ GL(C n ), there is an algorithm, by M. van Hoeij and J.-A. Weil, which computes the associated evaluation of the invariants ev :The procedure proposed here does the opposite: it uses a theorem of E. Compoint and computes the operator L from a given evaluation h. Moreover it solves a part of the inverse problem of producing L for a given representation of a finite group G. Another part considered here, is finding irreducible G-invariant curves Z ⊂ P(C n ) with Z/G of genus zero and constructing evaluations from this. The theory developed here is illustrated by various examples, and relates to and continues classical work of H.

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Section: Introductionmentioning

confidence: 57%

“…This method was refined in [vdP-U]. Klein's theorem is generalized in, e.g., [Ber,S1,S2,S3]. For (ii) there are many papers [S-U, Ho, H-W].…”

Section: Introductionmentioning

confidence: 99%

Linear differential equations with finite differential Galois group

2020

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“…. , n, then the correspondence between homogeneous invariants and solutions to the symmetric power [19] implies that for every P ∈ K[Y 1 , . .…”

Section: Gauge Equivalence and Invariantsmentioning

confidence: 99%

“…To overcome the difficulty of the extensive computations required in the algebraic case in Kovacic's algorithm, M. Berkenbosch applied in [4] this result of Klein and he generalized it to order three by introducing the concept of standard equations. Furthermore, C. Sanabria in [37] extended it to arbitrary order. Therefore, the problem of finding closed form solutions to algebraic linear ordinary differential equations has been reduced to the problem of first, characterizing the family of standard equations, and second, identifying which standard equation is needed in order to obtain closed form solutions to a given equation.…”

Section: Introductionmentioning

confidence: 99%