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The local analytic classification and the description of the Galois group forcomplex linear analytic q-difference equations have been obtained by Ramis,Sauloy and Zhang [15, 14] under the assumption that the slopes of the Newtonpolygon are integral. In this work, we relax that assumption.

Th\'eorie analytique locale des \'equations aux $q$-diff\'erences de pentes arbitraires