### Arithmetic theory of q-difference equations

**di Vizio, L ***(CNRS, IMJ, Paris)*

Thursday 14 May 2009, 11:00-12:00

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#### Abstract

We propose a global theory of q-difference equations over a finite extension of the field of rational functions k(q).
In the first part of the talk we will give a definition of a q-difference analogue of the theory of G-functions and establish a regularity result for the associated operators, obtained as a combination of a q-analogue of the Andre'-Chudnovsky Theorem and Katz Theorem.
In the second part of the paper, we combine the results pf the forst part with some formal q-analog Fourier transformations, obtaining a statement on the irrationality of special values of the formal q-Laplace transformation of a G_q-function.

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