A Skolem-Mahler-Lech Theorem in Positive Characteristic and Finite Automata
Number Theory
2007-05-23 v1 Commutative Algebra
Abstract
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.
Keywords
Cite
@article{arxiv.math/0510583,
title = {A Skolem-Mahler-Lech Theorem in Positive Characteristic and Finite Automata},
author = {Harm Derksen},
journal= {arXiv preprint arXiv:math/0510583},
year = {2007}
}
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43 pages