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Galois theory of \(q\)-difference equations: the “analytical” approach. (English) Zbl 1036.12007

Braaksma, B. L. J. (ed.) et al., Differential equations and the Stokes phenomenon. Proceedings of the conference, Groningen, Netherlands, May 28–30, 2001. Singapore: World Scientific, 277-292 (2002).
Summary: We show how a function theoretic approach to the Galois theory of Fuchsian \(q\)-difference equations (in contrast to the purely algebraic approach due to M. van der Put and M. F. Singer [Galois theory of difference equations. Lecture Notes in Mathematics. 1666. Berlin: Springer (1997; Zbl 0930.12006)] is possible and desirable. Based on classical complex geometry (theta functions and elliptic curves), it allows for a topological description of the Riemann-Hilbert-Birkhoff correspondence.
For the entire collection see [Zbl 1007.00033].

MSC:

39A13 Difference equations, scaling (\(q\)-differences)
34M55 Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies
12H10 Difference algebra

Citations:

Zbl 0930.12006
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