A Skolem¿Mahler¿Lech theorem in positive characteristic and finite automata

• Autores: Harm Derksen
• Localización: Inventiones mathematicae, ISSN 0020-9910, Vol. 168, Nº. 1, 2007, págs. 175-224
• Idioma: inglés
• DOI: 10.1007/s00222-006-0031-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.