Skolem–Mahler–Lech type theorems and Picard–Vessiot theory

Wibmer, Michael. "Skolem–Mahler–Lech type theorems and Picard–Vessiot theory." Journal of the European Mathematical Society 017.3 (2015): 523-533. <http://eudml.org/doc/277614>.

@article{Wibmer2015,
abstract = {We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem–Mahler–Lech theorem to rational function coefficients. The second problem is whether or not for a given linear difference equation there exists a Picard–Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell–Lang conjecture. This allows us to deduce solutions to the first two problems in a particular but fairly general special case.},
author = {Wibmer, Michael},
journal = {Journal of the European Mathematical Society},
keywords = {linear difference equations; Picard–Vessiot theory; Skolem–Mahler–Lech theorem; dynamical Mordell–Lang conjecture; linear difference equations; Picard-Vessiot theory; Skolem-Mahler-Lech theorem; dynamical Mordell-Lang conjecture},
language = {eng},
number = {3},
pages = {523-533},
publisher = {European Mathematical Society Publishing House},
title = {Skolem–Mahler–Lech type theorems and Picard–Vessiot theory},
url = {http://eudml.org/doc/277614},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Wibmer, Michael
TI - Skolem–Mahler–Lech type theorems and Picard–Vessiot theory
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 3
SP - 523
EP - 533
AB - We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem–Mahler–Lech theorem to rational function coefficients. The second problem is whether or not for a given linear difference equation there exists a Picard–Vessiot extension inside the ring of sequences. The third problem is a certain special case of the dynamical Mordell–Lang conjecture. This allows us to deduce solutions to the first two problems in a particular but fairly general special case.
LA - eng
KW - linear difference equations; Picard–Vessiot theory; Skolem–Mahler–Lech theorem; dynamical Mordell–Lang conjecture; linear difference equations; Picard-Vessiot theory; Skolem-Mahler-Lech theorem; dynamical Mordell-Lang conjecture
UR - http://eudml.org/doc/277614
ER -