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Differential Galois realization of double covers

Teresa Crespo, Zbigniew Hajto (2002)

Annales de l’institut Fourier

An effective construction of homogeneous linear differential equations of order 2 with Galois group 2 A 4 , 2 S 4 or 2 A 5 is presented.

Differential Galois Theory for an Exponential Extension of ( ( z ) )

Magali Bouffet (2003)

Bulletin de la Société Mathématique de France

In this paper we study the formal differential Galois group of linear differential equations with coefficients in an extension of ( ( z ) ) by an exponential of integral. We use results of factorization of differential operators with coefficients in such a field to give explicit generators of the Galois group. We show that we have very similar results to the case of ( ( z ) ) .

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