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SUMMARY:Arithmetic theory of q-difference equations - di Vizio\, L (CNRS\,
  IMJ\, Paris)
DTSTART:20090514T100000Z
DTEND:20090514T110000Z
UID:TALK18396@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We propose a global theory of q-difference equations over a fi
 nite extension of the field of rational functions k(q). \n\nIn the first p
 art of the talk we will give a definition of a q-difference analogue of th
 e theory of G-functions and establish a regularity result for the associat
 ed operators\, obtained as a combination of a q-analogue of the Andre'-Chu
 dnovsky Theorem and Katz Theorem. \n\nIn the second part of the paper\, we
  combine the results pf the forst part with some formal q-analog Fourier t
 ransformations\, obtaining a statement on the irrationality of special val
 ues of the formal q-Laplace transformation of a G_q-function. 
LOCATION:Satellite
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