A Skolem-Mahler-Lech Theorem in Positive Characteristic and Finite Automata

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dc.creatorDerksen, Harm
dc.date2005-10-27
dc.date.accessioned2026-07-07T06:47:58Z
dc.date.available2026-07-07T06:47:58Z
dc.descriptionLech 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.
dc.description43 pages
dc.identifierhttps://arxiv.org/abs/math/0510583
dc.identifierhttp://arxiv.org/abs/math/0510583
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103830
dc.subjectNumber Theory
dc.subjectCommutative Algebra
dc.subject11B37; 11B85; 68Q70
dc.titleA Skolem-Mahler-Lech Theorem in Positive Characteristic and Finite Automata
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