Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series)

Details Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series) Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series)

2009-02-24

arxiv.org/abs/0902.4169v3

Mathematics

Number Theory

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Scientific paper

In the first part of the paper we give a definition of G_q-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, \S 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 G_q-function.

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