Derksen, Harm and Masser, David.
(2015)
* Linear equations over multiplicative groups, recurrences, and mixing II.*
Indagationes Mathematicae , 26 (1).
pp. 113-136.

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Official URL: http://edoc.unibas.ch/41297/

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## Abstract

Let u1,…,umu1,…,um be linear recurrences with values in a field KK of positive characteristic pp. We show that the set of integer vectors (k1,…,km)(k1,…,km) such that u1(k1)+⋯+um(km)=0u1(k1)+⋯+um(km)=0 is pp-normal in a natural sense generalizing that of the first author, who proved the result for m=1m=1. Furthermore the set is effectively computable if KK is. We illustrate this with an example for m=4m=4. We also show that the corresponding set for zero characteristic is not decidable for m=557844m=557844, thus verifying a conjecture of Cerlienco, Mignotte, and Piras.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik 05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Zahlentheorie (Masser) |
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UniBasel Contributors: | Masser, David |

Item Type: | Article, refereed |

Article Subtype: | Research Article |

Publisher: | Elsevier |

ISSN: | 0019-3577 |

Note: | Publication type according to Uni Basel Research Database: Journal article |

Identification Number: | |

Last Modified: | 25 Aug 2016 07:03 |

Deposited On: | 25 Aug 2016 07:03 |

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