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

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 3, page 523-533
- ISSN: 1435-9855

## Access Full Article

top## Abstract

top## How to cite

topWibmer, 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.