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Basic Modern Theory of Linear Complex Analytic $q$-Difference Equations
About this Title
Jacques Sauloy
Publication: Mathematical Surveys and Monographs
Publication Year:
2024; Volume 287
ISBNs: 978-1-4704-7840-7 (print); 978-1-4704-7892-6 (online)
DOI: https://doi.org/10.1090/surv/287
Table of Contents
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Front/Back Matter
Chapters
- Prelude
- Elementary special and $q$-special functions
- Basic notions and tools
- Equations of low order, elementary approach
- Resolution of (general) scalar equations and factorisation of $q$-difference operators
- Further analytic properties of solutions: Index theorems, growth
- Equations and systems
- Systems and modules
- Further algebraic properties of $q$-difference modules
- Newton polygons and slope filtrations
- Fuchsian $q$-difference equations and systems: Local study
- Fuchsian $q$-difference equations and systems: Global study
- Galois theory of Fuchsian systems
- Irregular equations
- Irregular systems
- Some classical special functions
- Riemann surfaces and vector bundles
- Classical hypergeometric functions
- Basic index theory
- Cochain complexes
- Base change and tensor products (and some more facts from linear algebra)
- Tannaka duality (without schemes)
- Äech cohomology of abelian sheaves
- Äech cohomology of nonabelian sheaves
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