Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series)
Number Theory
2010-01-13 v3 Quantum Algebra
Abstract
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 -Borel transformation of a G_q-function.
Keywords
Cite
@article{arxiv.0902.4169,
title = {Arithmetic theory of q-difference equations (G_q-functions and q-difference modules of type G, global q-Gevrey series)},
author = {Lucia Di Vizio},
journal= {arXiv preprint arXiv:0902.4169},
year = {2010}
}
Comments
This paper won't be submitted for publication since the results below can be obtained in a more direct way