Arithmetic theory of q-difference equations (Gq-functions and q-difference modules of type G, global q-Gevrey series)
Abstract
In the first part of the paper we give a definition of Gq-function and we establish a regularity result, obtained as a combination of a q-analogue of the Andre'-Chudnovsky Theorem [And89, VI] and Katz Theorem [Kat70, 13]. In the second part of the paper, we combine it with some formal q-analogous Fourier transformations, obtaining a statement on the irrationality of special values of the formal q-Borel transformation of a Gq-function.
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