Twisted rational zeros of linear recurrence sequences
Abstract We introduce the notion of a twisted rational zero of a nondegenerate linear recurrence sequence (LRS). We show that any nondegenerate LRS has only finitely many such twisted rational zeros. In the particular case of the Tribonacci sequence, we show that and are the only twisted rational zeros that are not integral zeros.
Authors
- Florian Luca (ORCID: https://orcid.org/0000-0003-1321-4422)
- Joris Nieuwveld (ORCID: https://orcid.org/0009-0002-0339-1230)
- Yuri Bilu
- Joël Ouaknine (ORCID: https://orcid.org/0000-0003-0031-9356)
- James Worrell (ORCID: https://orcid.org/0000-0001-8151-2443)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université de Bordeaux (FR)
- Stellenbosch University (ZA)
- University of Oxford (GB)
- Max Planck Institute for Software Systems (DE)
- Science Oxford (GB)
- Institut de Mathématiques de Bordeaux (FR)
Publication Details
- Journal
- Journal of the London Mathematical Society
- Published
- 2025-03-01
- DOI
- https://doi.org/10.1112/jlms.70126
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft
- Agence Nationale de la Recherche