Galois Theories of Linear Difference Equations: An Introduction
About this Title
Charlotte Hardouin, Institut de Mathématiques de Toulouse, Toulouse, France, Jacques Sauloy, Institut de Mathématiques de Toulouse, Toulouse, France and Michael F. Singer, North Carolina State University, Raleigh, NC
Publication: Mathematical Surveys and Monographs
Publication Year: 2016; Volume 211
ISBNs: 978-1-4704-2655-2 (print); 978-1-4704-2940-9 (online)
MathSciNet review: MR3410204
MSC: Primary 12H10; Secondary 39-01, 39A10, 39A13
This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.
Graduate students and researchers interested in algebraic constructions in the theory of differential and difference equations.
Table of Contents
- Michael F. Singer – Algebraic and algorithmic aspects of linear difference equations
- Charlotte Hardouin – Galoisian approach to differential transcendence
- Jacques Sauloy – Analytic study of $q$-difference equations