# Galois theories for $q$-difference equations: comparison theorems

Abstract : We establish some comparison results among the different Galois theories, parameterized or not, for q-difference equations, completing the work of Chatzidakis-Hardouin-Singer. Our main result is the link between the abstract parameterized Galois theories, that give information on the differential properties of abstract solutions of $q$-difference equations, and the properties of meromorphic solutions of such equations. Notice that a linear q-difference equation with meromorphic coefficients always admits a basis of meromorphic solutions.
Document type :
Journal articles

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Submitted on : Tuesday, February 26, 2013 - 2:41:45 PM
Last modification on : Monday, September 12, 2022 - 9:13:48 AM

### Citation

Lucia Di Vizio, Charlotte Hardouin. Galois theories for $q$-difference equations: comparison theorems. Confluentes Mathematici, Institut Camille Jordan et Unité de Mathématiques Pures et Appliquées, 2020, 12 (2), pp.11--35. ⟨10.5802/cml.66⟩. ⟨hal-00794745⟩

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