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

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

2005-10-27

arxiv.org/abs/math/0510583v1

Mathematics

Number Theory

43 pages

Scientific paper

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.

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