# 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 :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-00794745
Submitted on : Tuesday, February 26, 2013 - 2:41:45 PM
Last modification on : Friday, April 10, 2020 - 5:08:51 PM

### Identifiers

• HAL Id : hal-00794745, version 1
• ARXIV : 1205.1696

### Citation

Lucia Di Vizio, Charlotte Hardouin. Galois theories for $q$-difference equations: comparison theorems. 2012. ⟨hal-00794745⟩

Record views