2006/09/22 by Charlotte Hardouin, Hardouin, Charlotte · 1 citation
Computer Science · Mathematics · #11 R 34 #12 H 05 #12 H 10 #34 M 15 #39 A 13 #Algebraic Geometry and Number Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Polynomial and algebraic computation #Quantum Algebra (math.QA) #math.CA #math.QA #msc:05 #msc:10 #msc:11 #msc:12 #msc:13 #msc:15 #msc:34 #msc:39
paper · pdf · doi:10.48550/arxiv.math/0609646
42 pages
openalex publication_date 2006/09/22 · arxiv created 2006/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper deals with criteria of algebraic independence for the derivatives of solutions of rank one difference equations. The key idea consists in deriving from the commutativity of the differentiation and difference operators a sequence of iterated extensions of the original difference module, thereby setting the problem in the framework of difference Galois theory and finally reducing it to an exercise in linear algebra. The involved tannakian categories are neutral over non necessarily algebraically closed fields, and this leads us to study the behaviour of Galois groups under base field extensions.