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Journal Articles Confluentes Mathematici Year : 2020

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


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.

Dates and versions

hal-00794745 , version 1 (26-02-2013)



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