2012/03/07 by Michael Wibmer, Wibmer, Michael
Mathematics · #11B25 #11B37 #12H10 #39A05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AC #math.AG #math.DS #msc:11B25 #msc:11B37 #msc:12H10 #msc:39A05
paper · pdf · doi:10.48550/arxiv.1203.1449
arxiv created 2012/03/07 · arxiv updated 2012/03/08
We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem-Mahler-Lech theorem to rational function coefficients. The second problem is the question whether or not for a given linear difference equation there exists a Picard-Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell-Lang conjecture. This allows us to deduce solutions to the first two problems in a particular but fairly general special case.