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Scarcity of finite orbits for rational functions over a number field

Title data

Canci, Jung Kyu ; Troncoso, Sebastian ; Vishkautsan, Solomon:
Scarcity of finite orbits for rational functions over a number field.
In: Acta Arithmetica. Vol. 190 (2019) Issue 3 . - pp. 221-237.
ISSN 0065-1036
DOI: https://doi.org/10.4064/aa180210-4-12

Abstract in another language

Let ϕ be an endomorphism of degree d≥2 of the projective line, defined over a number field K. Let S be a finite set of places of K, including the archimedean places, such that ϕ has good reduction outside S. The article presents two main results. The first result is a bound on the number of K-rational preperiodic points of ϕ in terms of the cardinality of S and the degree d of ϕ. This bound is quadratic in d, which is a significant improvement to all previous bounds in terms of d. The second result is that if there is a K-rational periodic point of period at least 2, then there exists a bound on the number of K-rational preperiodic points of ϕ that is linear in d.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: preperiodic points; periodic; arithmetic dynamics
Subject classification: MSC: Primary 37P05, 37P35; Secondary 11D45
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics II (Computer Algebra)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 27 Oct 2020 13:09
Last Modified: 27 Oct 2020 13:09
URI: https://eref.uni-bayreuth.de/id/eprint/58782