2005/10/27 by Harm Derksen, Derksen, Harm · 2 citations
Computer Science · Mathematics · #11B37 #11B85 #68Q70 #Advanced Algebra and Logic #Algorithm #Automaton #Cellular automaton #Commutative Algebra (math.AC) #Computer science #Discrete mathematics #FOS: Mathematics #Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Pure mathematics #Theoretical computer science #math.AC #math.NT #msc:11B37 #msc:11B85 #msc:68Q70 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0510583
published in arXiv (Cornell University) (Cornell University) · 43 pages
arxiv created 2005/10/27 · openalex publication_date 2005/10/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Lech proved in 1953 that the set of zeroes of a linear recurrence sequence in a field of characteristic 0 is the union of a finite set and finitely many infinite arithmetic progressions. This result is known as the Skolem-Mahler-Lech theorem. Lech gave a counterexample to a similar statement in positive characteristic. We will present some more pathological examples. We will state and prove a correct analog of the Skolem-Mahler-Lech theorem in positive characteristic. The zeroes of a recurrence sequence in positive characteristic can be described using finite automata.