# Differential Galois Theory for an Exponential Extension of $\u2102\left(\right(z\left)\right)$

Bulletin de la Société Mathématique de France (2003)

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

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topBouffet, 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

top- [1] M. Bouffet – « Un lemme de Hensel pour les opérateurs différentiels », 331 (2000), no. 4, p. 277–280. Zbl1014.12006MR1787185
- [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] A. Magid – Lectures on Differential Galois Theory, University Lecture Series, vol. 7, American Math. Society, 1994. Zbl0855.12001MR1301076

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