Galois Theories of Linear Difference Equations: An Introduction

Charlotte Hardouin (1) , Jacques Sauloy (1) , Michael F. Singer (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 NCSU - Department of Mathematics [Raleigh]

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.

Domaines: Algèbre commutative [math.AC]; Géométrie algébrique [math.AG]; Systèmes dynamiques [math.DS]; Théorie des nombres [math.NT]

Charlotte Hardouin, Jacques Sauloy, Michael F. Singer. Galois Theories of Linear Difference Equations: An Introduction. American Mathematical Society. American Mathematical Society, 211, 2016, Mathematical Surveys and Monographs, 978-1-4704-2655-2. ⟨10.1090/surv/211⟩. ⟨hal-01959879⟩