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

Magali Bouffet

Bulletin de la Société Mathématique de France (2003)

  • Volume: 131, Issue: 4, page 587-601
  • ISSN: 0037-9484

Abstract

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In this paper we study the formal differential Galois group of linear differential equations with coefficients in an extension of ℂ ( ( 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 ℂ ( ( z ) ) .

How to cite

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Bouffet, Magali. "Differential Galois Theory for an Exponential Extension of $\mathbb {C}((z))$." Bulletin de la Société Mathématique de France 131.4 (2003): 587-601. <http://eudml.org/doc/272314>.

@article{Bouffet2003,
abstract = {In this paper we study the formal differential Galois group of linear differential equations with coefficients in an extension of $\mathbb \{C\}((z))$ 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 $\mathbb \{C\}((z))$.},
author = {Bouffet, Magali},
journal = {Bulletin de la Société Mathématique de France},
keywords = {differential Galois theory; linear differential equations; exponential extension; universal differential extension; differential Galois group},
language = {eng},
number = {4},
pages = {587-601},
publisher = {Société mathématique de France},
title = {Differential Galois Theory for an Exponential Extension of $\mathbb \{C\}((z))$},
url = {http://eudml.org/doc/272314},
volume = {131},
year = {2003},
}

TY - JOUR
AU - Bouffet, Magali
TI - Differential Galois Theory for an Exponential Extension of $\mathbb {C}((z))$
JO - Bulletin de la Société Mathématique de France
PY - 2003
PB - Société mathématique de France
VL - 131
IS - 4
SP - 587
EP - 601
AB - In this paper we study the formal differential Galois group of linear differential equations with coefficients in an extension of $\mathbb {C}((z))$ 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 $\mathbb {C}((z))$.
LA - eng
KW - differential Galois theory; linear differential equations; exponential extension; universal differential extension; differential Galois group
UR - http://eudml.org/doc/272314
ER -

References

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  1. [1] M. Bouffet – « Un lemme de Hensel pour les opérateurs différentiels », 331 (2000), no. 4, p. 277–280. Zbl1014.12006MR1787185
  2. [2] —, « Factorisation d’opérateurs différentiels à coefficients dans une extension liouvillienne d’un corps valué », Ann. Inst. Fourier 52 (2002), no. 3, p. 709–734. Zbl1017.12006MR1907385
  3. [3] A. Magid – Lectures on Differential Galois Theory, University Lecture Series, vol. 7, American Math. Society, 1994. Zbl0855.12001MR1301076

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