Algebraic periodic points of transcendental entire functions
We prove the existence of transcendental entire functions f having a property studied by Mahler, namely that [Formula: see text] and [Formula: see text], and in addition having a prescribed number of k-periodic algebraic orbits, for all [Formula: see text]. Under a suitable topology, such functions are shown to be dense in the set of all entire transcendental functions.
Authors
- David Krumm (ORCID: https://orcid.org/0000-0001-9999-2166)
- Pavel Trojovský (ORCID: https://orcid.org/0000-0001-8992-125X)
- Diego Marques (ORCID: https://orcid.org/0000-0002-5663-3785)
- Carlos Gustavo Moreira (ORCID: https://orcid.org/0000-0003-3689-7529)
Institutions
- Instituto Nacional de Matemática Pura e Aplicada (BR)
- Universidade de Brasília (BR)
- Universidad de Costa Rica (CR)
- University of Hradec Králové (CZ)
Publication Details
- Journal
- International Journal of Number Theory
- Published
- 2024-11-15
- DOI
- https://doi.org/10.1142/s1793042125500472
- Primary Topic
- Meromorphic and Entire Functions
- Type
- article
- Field-Weighted Citation Impact
- 0.00